Thermodynamics Problem Set With Solutions
Thermodynamics Problem Set With Solutions
Thermodynamics Problem Set With Solutions
MULTIPLE CHOICE
1. A spherical tank is full of water that has a mass of 10 000 kg. If the outside diameter of the tank is 2722 mm,
how thick is the wall of the tank?
m
ρ
V
10,000 3
V 1000 10 m
3
4πr
V
3
r 1.337 m
d 2(1.337) 2.674 m 2674 mm
2722 - 2674
t 2 24 mm
2. A cylindrical tank is filled with water at the rate of 5000 Gal/min. The height of water in the tank after 15 minutes
is 20.42 ft. What is the diameter of the tank? (Note: 1 ft 3 = 7.481 Gallons)
V 5000 (15) 75000 10,025.4 ft 3
Gallons
π 2
V D H; H 20.42 ft
4
D 25 ft
3. At what temperature in which the reading in Fahrenheit scale is the same as the Centigrade scale.
Conversion
F 32
C 1.8
F 1.8(C)
32 x C F
x 32
x 1.8
x 40
4. A new temperature scale is desired with freezing point of water at 0 X and boiling occurring at 1000X. Derive
the conversion between C and X and what is 0K in X.
1000 0
100 0 10
m 10
y mx b
K C 273
0K C 273
C -273
X 10(273) 0
X 2730
5. A pressure gage at elevation 8 m on the side of a tank containing a liquid reads 57.4 KPa. Another gage at
elevation 5 m reads 80 KPa. Compute the specific weight and density of the liquid. (use g = 9.81 m/sec2)
ΔP γ(Δh)
(57.4 80) γ(8 5)
KN
γ 7.53
m3
ρg
γ 1000
kg
ρ 767.9
m3
6. An open tank contains 5 m of water covered with 2 m of oil ( = 8 KN/m3). Find the absolute pressure at the at
the bottom of the tank. (Assume Patm = 101 KPa)
101 (2)(8) 5(9.81) PBottom
PBottom 166.05KPa
7. A skin diver wants to determine the pressure exerted by the water on her body after a descent of 35 m to a
sunken ship. The specific gravity of seawater is 1.02 times that of pure water. Determine the pressure in KPa.
P 0 35(1.02)(9.81)
8. A water storage tank contains liquid and vapor in equilibrium at 250C,(l = 799.23 m3/kg; v = 19.95
m3/kg).The distance from the bottom of the tank to the liquid level is 10 m. What is the difference in
pressure reading
between the top of the tank and the bottom of the tank if the vapor pressure is 3,973 KPa. (Assume g = 9.81
m/sec2)
-27
9. Compute the gravitational force between a proton ( m = 1.66 x 10 kg) and an electron (m = 9.11 x 10-31 kg)in
an atom whose radius of electron orbit is 5.29 x 10-11 m.
Gm1m2
Fg Newton
r2
11 27 31
6.67(10 )(1.66)(10 )(9.11)(10 )
Fg 1.9x10 Newton
11
5.29(10 ) 43
10. A pressure in the cylinder in the figure varies in the following manner with volume, P = C/V2. If the initial
pressure is 500 KPa, initial volume is 0.05 m 3 and the final pressure is 200 KPa, find the work done by the
system.
F 32
C 1.8
F 1.8C 32
F 2C
2C 1.8C 32
C 32
160
2
1.8
F 320
12. A cylindrical tank 2 m diameter, 3 m high is full of oil. If the specific gravity of oil is 0.9, what is the mass of oil in
the tank? (8482.3 kg)
π 2 π 2 3
V DH (2 )3 3π m
cylinder
ρ 4 4
S
ρwater
0.9 ρ
1000
kg
ρ 900
m3
m
ρ
V
m 900(3π) 8482.3 kg
13. 10 liters of an incompressible liquid exert a force of 20 N at the earth’s surface. What force would 2.3 Liters of
this liquid exert on the surface of the moon? The gravitational acceleration on the surface of the moon is 1.67
m/sec2.
F ma
m
V
1m3
m V (10.0) 1000L kg
(10.0)
20 9.81N
1000
kg
203.874
m3
On the surfaceof the moon
F 203.874
2.3 (1.67)
0.783 N
1000
14. If the temperature inside a furnace is 700 K, what is the corresponding reading in F? (800.6)
Solution:
t = 700 – 273 = 427C
F = (427)(1.8) + 32
F = 800.6F
15. A storage tank contains oil with a specific gravity of 0.88 and depth of 20 m. What is the hydrostatic pressure at
the bottom of the tank in kg/cm2.(1.7)
Solution:
Using: g = 9.81 m/sec2
0.88(1000)(9.81)(20)
P0 172.656 KPa
1000
2
P = 1.7 kg/cm
16. A hiker carrying a barometer that measures 101.3 KPa at the base of the mountain. The barometer reads 85
KPa at the top of the mountain. The average air density is 1.21 kg/m3. Determine the height of the mountain.
dP γdh
P2 P1 γ(h2 h1)
h 2 h1 h
(P1 P2 )1000
h ρg
(101.3 85)1000
h 1.21(9.81)
h 1373 m
17. Water runs through a water main of cross sectional area of 0.4 m 2 with a velocity of 6 m/sec. Calculate the
velocity and mass flow rate of the water in the pipe when the pipe tapers down to a cross sectional area of 0.3
m2. ( = 1000 kg/m3)
m1 m2 m
A1v1 m
m 1000(0.4)6 2400 kg
sec
A1v1 A 2 v 2
Av
v 1 1 8 m
2
A2
sec
18. The 600 kg hammer of a pile driver is lifted 2 m above the piling head. What is the change in potential energy?
If the hammer is released, what will be its velocity at the instant it strikes the filing? Local g =9.65 mps2.(11.58
KJ; 6.21 mps)
m = 600 kg
Z = 2 m
g = 9.65 m/sec2
mgZ
PE KJ
1000
PE 11.58 KJ
KE = PE
2 2
m(v f v i )
11.58
2(1000)
vi 0
11.58(2000)
vf m
600 6.21
sec
19. A lump of ice falls from an aero plane as it comes into land. If the ice hits the ground with a vertical speed of 85
m/sec, what was the height of the plane when the ice fell off? (use g = 9.81 m/sec 2)
ΔKE 2 ΔPE
m85 0 mg0 h
h 2(1000) 1000
h 368.25 meters
20. 5 kg of brass of specific heat 0.39 KJ/kg -C at a temperature of 176C is dropped into a 1.2 kg of water at
14C. Find the resulting temperature of the mixture. (C PW = 4.187 KJ/kg -C)
mw 1.2 kg
mB 5 kg
CPB KJ
0.39
kg -
C
CPW KJ
4.187
kg -
C
Heat rejectedby brass Heat absorbedby water
QB QW
mBCPB (tB1 t) mw CPW (t tw1 )
5(0.39)(176 t) 1.2(4.187)(t 14)
t 40.4C
21. How much heat is removed to make ice of mass m = 0.720 kg at -10C from a liquid at 15C.
Specific heat of ice = 2.22 KJ/kg-C
Specific heat of water = 4.19 KJ/kg-C
Freezing point temperature of water = 0C
hF of ice = 334.9 KJ/kg
Answer: 302 KJ
Q Q1 Q2 Q3
Q1 mCpw (15 0) sensibleheat
Q2 m(hF ) latent heat
Q3 mCpi (0 10) sensibleheat
Q 0.7204.19(15- 0) (334.9) 2.22(0 10)
Q 302 KJ
22. A steam turbine receives superheated steam at 1.4 MPa and 400C (h1 = 3257.5 KJ/kg). The steam leaves the
turbine at 0.101 MPa and 100C (h2 = 2676 KJ/kg).The steam enters the turbine at v1 = 15 m/sec and exits at
v2 = 60 m/sec. The elevation difference between entry and exit ports is negligible. The heat loss through the
turbine walls is 2 KW. Calculate the power output if the mass flow through the turbine is 0.5 kg/sec.
Q h KE PE W
h m(h2 h1 ) 290.75 KW
2 2
23. Steam with a flow rate of 1360 kg/hr enters an adiabatic nozzle at 1378 KPa, 3.05 m/sec with a specific volum
e of 0.147 m3/kg and with a specific internal energy of 2510 KJ/kg. The exit conditions are, P = 137.8 KPa,
specific volume = 1.099 m3/kg, and internal energy = 2263 KJ/kg. Determine the exit velocity in m/sec.
Given:
m = 1360 kg/hr = 0.377 kg/sec P2 = 137.8 KPa
P1 = 1378 KPa 2 = 1.099 1 2
m3/kg
v1 = 3.05 m/sec U2 = 2263 KJ/kg
1 = 0.147 m3/kg
For Adiabatic Q = 0 and for
U1 = 2510 KJ/kg a Nozzle W = 0
1 2
Wt
24. A small steam turbine operating at part load produces 110 KW output with a steam flow rate of 0.25 kg/sec.
Steam at 1.4 MPa, 250C is throttled to 1.1 MPa before entering the turbine, and the turbine exhaust pressure
is 10 KPa. Find the steam quality (or temperature, if superheated) at the turbine outlet. (x 2 = 96%)
From table 3 at 1.4 MPa and 250C: h = 2927.2 KJ/kg
From table 2 at 10 KPa (0.010 MPa): hf = 191.83 KJ/kg; hfg = 2392.8 KJ/kg
Q h KE PE W
0 h KE 0 0
KE h
2 2
v 2 v 1
(h 2 h1 )
2(1000)
2
v 2 2(1000)(h1 h2 ) v1
h U P
h1 2510 (1378)(0.147) 2712.6 KJ/kg
h2 2263 (137.8)(1.099) 2401.9 KJ/kg
kg v 2 788.3 m/sec
m
0.25 sec
KJ
h1 h2 2927.2
kg
Q h KE PE W
Q 0; KE 0 and PE
0 W -h
110 m(h2 - h3 )
h3 h2 110
- m
KJ
h 2487.2
3
kg
h hf x(hfg )
2487.2- 191.83
x 3 2392.8 0.96
x3 96%
25. A throttling calorimeter is connected to the de-superheated steam line supplying steam to the auxiliary feed
pump of a ship. The line pressure measures 2.5 MPa. The calorimeter pressure is 110 KPa and the
temperature is 150C. Determine the line steam quality.
From Superheated table, at 110 KPa and 150C, h2 = 2775.6 KJ/kg
From Saturated liquid and saturated vapor table
hf1 = 962.11 KJ/kg; hfg = 1841.0 KJ/kg
h1 = hf1 + x1(hf g1)
h1 = h2
h1 hf1 2775.6 962.11
x1
hfg1 1841.0 0.985
x1 98.5%
26. An engineering student wants to cool 0.25 kg of Omni Cola (mostly water) initially at 20C by adding ice that is
initially at -20C. How much ice should be added so that the final temperature will be 0C with all the ice
melted, if the heat capacity of the container neglected.
Cwater = 4.19 KJ/kg-C
Cice = 2.010 KJ/kg-C
hf of ice = 334.9 KJ/kg
Qcola = Qice
0.25(4.19)(20 – 0) = mice[(2.010)(0 + 20) + 334.9]
mice = 0.056 kg = 56 gram
27. 2.5 kg of brass of specific heat 0.39 KJ/kg-K at a temperature of 176C is dropped into a 1.2 liters of water at
14C. Find the resulting temperature of the mixture. (At 14C density of water is 999 kg/m3)
v
VL
0.002222
f
mL
0.0425
mL 19.13 kg
0.002222
VV
v
g
0.004193
mV
0.0425
mV 10.14 kg
0.004193
b.
VL VV 0.085
VL 0.085 VV eq.1
VL
v
f
mL
0.085 V
mL 0.00222V eq. 2
V
v V
g
mV
VV
m eq. 3
V
0.004193
mL mV
0.085 VV
VV
0.00222 0.004193
VV 0.085(0.004193)
0.002222 0.004193
3
VV 0.056 m
3
VL 0.029 m
29. An industrial power plant requires 1.5 kg of dry saturated steam per second at 165C for heating purposes. This
steam may be supplied from an extraction turbine which receives steam at 4 MPa and 380C and is exhausted
to a condenser at the rate of 0.8 kg/sec at 0.0034 MPa while rejecting 1400 KW to the cooling water. If the
mechanical efficiency of the turbine generator unit is 95% and the heat loss in the turbine casing is 10 KW,
calculate the power generated by the plant.
(Wo = 1540 KW)
h at 4 MPa and 380C = 3165.9 KJ/kg
hg at 165C = 2763.5 KJ/kg
hf at 0.0034 MPa = 109.84 KJ/kg
h1 P1 = 4 Mpa t1 = 380C
m= 10 KW
Generator Efficiency = 94%
1
1.5 kg/sec 2
30.8 kg/sec
h2 165 C
QR = 1400 KW
4 h4
By mass balance
kg
m 1.5 0.8 sec
2.3
By energybalancecondenser
QR 0.8(h3 h4 )
1400 0.8(h3 109.84)
KJ
h 1859.84
3
kg
By energybalancein the turbine
2.3(3165.9) - 10 - 1.5(2763.5) - 0.8(1859.84)
Wt Wt 1638.45KW
WOUTPUT 1540.14 KW
30. Steam enters a turbine with a velocity of 1.5 m/sec and an enthalpy of 2093 KJ/kg and leaves with an enthalpy
of 1977 KJ/kg and a velocity of 91.5 m/sec. Heat losses are 8 KCal/min and the steam flow rate is 27 kg/min.
The inlet of the turbine is 3.5 m higher than its outlet. What is the work output of the turbine if the mechanical
losses is 15%
a) 32.4 KW b) 24.3 KW c) 34.2 K d) 48 KW
v1 1.5
m
sec
v2 91.5 m
sec
kg kg
m 27 0.45
min sec
KCal
Q8 x KJ 1min
4.187 min 0.56 KW (rejected)
KCalx 60
sec
z1 0
z2 -3.5 m
KJ
h 2093
1
kg
KJ
h 1977
2
kg
2 2
m(v v )
KE 2 1 1.883 KW
2(1000)
h m(h2 h1) 52.2 KW KW
mg(z2 z1)
PE 0.015 KW
1000
Q h KE PE W
W Q (h KE PE) 49.77 KW
Power Output 49.77(1- .15) 42.3
KW
31. An air compressor handles 8.5 m3/min of air with a density of 1.26 kg/m3 and a pressure of 101 KPaa and
discharges at 546 KPaa with a density of 4.86 kg/m 3. The changes in specific internal energy across the
compressor is 82 KJ/kg and the heat loss by cooling is 24 KJ/kg. Neglecting changes in kinetic and potential
energies, find the work in KW.
m
V
m V 1.26(8.5) 10.71kg/min 0.1785kg/sec
Q U (P ) KE PE W
W Q - U - (P ) - KE - PE
W Q - (U2 - U1 ) - (P22 - P11 ) - 0 - 0
P P
W Q - (U2 - U1 ) - 2 1
2 1
546 101 KJ
W (24) (82) 138.2
In KW 4.86 1.26 kg
W 0.1785(-138.2) 24.67 KW
W 24.67KW (Work is doneon the system)
32. Calculate the change of entropy per kg of air when heated from 300K to 600K while the pressure drops from
400 Kpa to 300 KPa. (S = 0.78 KJ/kg-K)
Given;
R = 0.287 KJ/kg-K
k = 1.4
T1 = 300K ; T2 = 600K
P1 = 400 KPa ; P2 = 300 KPal
T P
ΔS C ln 2 R ln 2
p
T1 P1
33. A certain mass of sulfur dioxide (SO 2) is contained in a vessel of 0.142 m3 capacity, at a pressure and
temperature of 2310 KPa and 18C, respectively. A valve is open momentarily and the pressure falls
immediately to 690 KPa. Sometime later the temperature is again 18C and the pressure is observed to be 910
KPa. Estimate the value of specific heat ratio. (k = 1.29)
8.3143
R 0.13
64
P1V1 m1RT1
2310(0.142)
m1 0.13(291) 8.67 kg
At V C
P1 P2
T1 T2
T 2P 86.92K
2
P1
T
1
34. Two unequal vessel A and B are connected by a pipe with a valve. Vessel A contains 150 L of air at 2760 KPa
and 95C. Vessel B contains an unknown volume of air at 70 KPa and 5C. The valve is opened and when the
properties have been determined, it was found out that the pressure of the mixture is 1380 KPa and the
temperature is 45C. What is the volume of vessel B.(0.166 m3)
Given:
VA = 0.150 m3 ; PA = 2760 KPa ; TA = 95 + 273 = 368 K
V VA VB
m mA mB
PV
m ; m PA VA ; m PB VB
A
RT RTA B RTB
1380(0.150 VB ) 2760(0.150) 70(VB )
R(318) R(368) R(278)
0.65 4.34VB 1.125 0.252VB
(1.125 0.65)
VB (4.34 0.252) 0.116 m3
35. A vessel of volume 0.2 m3 contains nitrogen at 101.3 KPa and 15C. If 0.2 kg of nitrogen is now pumped into
the vessel, calculate the new pressure when the vessel has returned to its initial temperature. For nitrogen: M
= 28; k = 1.399. (187 KPa) (Sample Prob. June 18, 2014)
Given :
3
V 0.2 m ; P 101.3KPa; T 15 273 288K
1 1 1
8.3143 KJ
R 28 kg -
K
m1 101.3(0.2)28
0.237 kg
8.3143(15
273)
m2 0.237 0.2 0.437 kg finalmass
T2 15 273 288K
mRT
P
V
V2 V1
0.437(8.3143)(15 273)
P2 186.82 KPa
28(0.2)
36. A certain perfect gas of mass 0.1 kg occupies a volume of 0.03 m 3 at a pressure of 700 KPa and a temperature
of 131C. The gas is allowed to expand until the pressure is 100 KPa and the final volume is 0.2 m 3. Calculate;
a) the molecular weight of the gas (16)
b) the final PV mRT
temperature Given; PV
R 1 1
m = 0.1 kg ; V1 = 0.03 m3 ; P1 = 700 KPa ; T1 = 131 +273 = 404 K mT1
P2 = 100 KPa ; V2 = 0.2 m3 KJ
R 0.52
kg - K
8.3143
R
M
8.3143 kg
M R 16
kgmol
PV
T C
P1V1 P2 V2
T1 T2
T1P2 V2
T2 384.8K
PV
11
t2 111.8C
37. An ideal gas with R = 2.077 KJ/kg-K and a constant k= 1.659 undergoes a constant pressure process during
which 527.5 KJ are added to 2.27 kg of the gas. The initial temperature is 38C. Find the S in KJ/K.
Given:
R = 2.077 KJ/kg-K; k = 1.659
Q = 527.5 KJ; m = 2.27 kg
T1 = 38 + 273 = 311 K
Process: P = C
RK
Cp 5.72KJ/kg K
k 1
Q = mCp(T2 – T1) ;
T2 Q
T1 352 K
mCp
T
S mCpln 2 1.6KJ/K
T1
38. A certain perfect gas of mass 0.1 kg occupies a volume of 0.03 m3 at a pressure of 700 KPa and a temperature
of 131C. The gas is allowed to expand until the pressure is 100 KPa and the final volume is 0.02 m 3.
Calculate;
a) the molecular weight of the gas (16)
b) the final temperature (11.5C)
0.1(8.3143)(131 273)
700(0.03) M
M 16
P2 V2mRT2
0.1(8.3143)(t2 273)
100(0.15) 16
t2 15.7C
39. What is the weight of a 114 L tank of oxygen (O2) if the oxygen is pressurized to 1.4 MPa, and the tank itself
weighs 445N, and the temperature is 10C.
8.3143
R 0.26 KJ
32
kg - K
PV mRT
1400(0.114)
m 0.26(10 2.17 kg
273)
W 2.17(9.81) 21.29 N
O2
40. Assume 2 kg of O2 are mixed with 3 kg of an unknown gas. The resulting mixture occupies a volume of 1.2 m3
a)
m = 5 kg
xO2 = 0.40 ; xx = 0.60
R = 0.1361 KJ/kg-K
R = .40(0.26) + 0.60(Rx)
Rx = 0.535 KJ/kg-K
Mx = 15.54 kg/kgm
b)
yO2 = 0.245 ; yx = 0.755
c) PO2 = .245(276) = 67.62 KPa ; Px = 0.755(276) = 208.38 KPa
41. How many kilograms of N2 must be mixed with 3.6 kg of CO2 in order to produce a gaseous mixture that is
50% by volume of each constituents.
Gas M k
CO2 44 1.288
N2 28 1.399
yN 0.50
2
yCO 0.502
yM
xi iM i
M 0.50(28) 0.50(44) 36
R 0.231
xN2
0.50(28)
36 0.389
xCO 1.389 0.611
2
xN mN mN
2
2
2
m mN mCO2 2
m
0.389 N 2
mN 3 2
(0.389)mN 0.389(3) m
2 2
mN
0.389(3)
(1 0.389) 1.91 kg
2
42. Three moles of oxygen is compressed in a piston cylinder assembly in a reversible adiabatic process from a
temperature of 300 K and a pressure of 102 KPa until the final volume is one tenth the initial volume. Determine
the final temperature and the final pressure.
Given; T1 = 300 K ; P1 = 102 KPa ;
V2 1 V ; V1 10
1
10 V2
T V
k k 1 k
; T T 1V
1
;P V k P V k; P V
2
1
1 P1 k
1
V
2
T V 1 1 2 2 2
V
1 2 2 2
For Oxygen; R = 0.2598 KJ/kg-K; k = 1.395
T2 = 745K ; P2 = 2532.8 KPa
43. Two kilograms of helium operates on a three process cycle where the processes are constant volume (1 to 2);
constant pressure (2 to 3); and constant temperature (3 to 1). Given that P 1 = 100 KPa, T1 = 300 K, and 1/3
= 5. Determine the pressure, specific volume and temperature around the cycle.
For Helium: R = 2.077 KJ/kg-K ; k = 1.666
Given: 2 to 3 (Isobaric: P = C)
P1 = 100 KPa ; T1 = 300 K ; 1/3 = 5 3 to 1 (Isothermal: T = C or PV = C)
Processes:
1 to 2 (Isometric: V = C) T2 P 2
P1υ1 100(6.231)
T1 P1 P3 500.5 KPa
υ3 1.245
υ1 υ2
P3 P2 500.5 KPa
RT1 2.077(300) 6.231m 3
υ1 T3 T1 300 K
P1 100 kg
m3
υ2 6.231
kg P 500.5
υ1 T2 T 1 2 300
5 P1 100
υ3 T2 1501.5 K
υ1
υ 6.231 1.245 m3
3
5 5 kg
P1υ1 P3 υ3
44. Oxygen expands in a reversible adiabatic manner through a nozzle from an initial pressure and initial
temperature and with an initial velocity of 50 m/sec. there is a decrease of 38K in temperature across the
nozzle. Determine
a. the exit velocity
b. for inlet conditions of 410 KPa and 320 K, find the exit pressure.
1 2
Given:
v1 = 50 m/sec Q h KE PE W
T = 38 K Q 0; W 0; and PE 0
P1 = 410 KPa ; T1 = 320 K KE h -Cp (T2 - T1 )
Fpr O2: Cp = 0.918 KJ/kg-K ; k = 1.395 2 2
v -v
2 1
-C p (T - T1 )
2000 2
46. A cylinder fitted with a frictionless piston contains 5 kg of superheated water vapor at 1000 KPa and 250C.
The system is now cooled at constant pressure until the water reaches a quality of 50%. Calculate the work
done and the heat transferred.
U
2 S = 6.9247 KJ/kg-C
= 0.2327 m3/kg
At 1000 KPa and x = 50% Sh = 1770.46 KJ/kg
U = 1672.64 KJ/kg
S = 4.3626 KJ/kg-C
Q = 0.097784 m3/kg
tsat = 179.91C
1
W m Pd mP( 2 1 ) 5(1000)(0.97784 0.2327) 674.58KJ (work is done on thesystem)
Q 5860.88 KJ(heatis rejected)
47. A 0.5 m3 tank contains saturated steam at 300 KPa. Heat is transferred until the pressure reaches 100 KPa.
Determine the heat transferred and the final temperature.
300 KPa 1
U
2
Q 100 KPa
Process: Constant Volume
W=0
Q = U
Q = m(U2 – U1)
48. A reversible nonflow constant volume process decreases the internal energy by 316.5 KJ for 2.3 kg of a gas for
which R = 0.47 KJ/kg-K and k = 1.35. For the process, determine
a. the work
b. the heat
c. the entropy change if the initial temperature is 478K
Given:
U = -316.5 KJ
m = 2.3 kg
R = 0.47 KJ/kg-K
k = 1.3
T1 = 478K
Solution
At V = C ; Q = U = mCv (T)
Cv R 0.47
1.567 KJ/kg - K
k 1 1.3
1
Q - 316.5 2.3(1.567)(T2 - 478)
T2 390K
a. W = PdV = 0
b. Q = -316.5 KJ
Q = 316.5 KJ (heat is rejected)
c.
T 390 KJ
S mCv ln 2 2.3(1.567)ln 0.733
T1 478 K
49. In a turbine 4500 kg/min of air expands polytropically from 425 KPa and 1360K to 101 KPa. The exponent n
= 1.45 for the process. Find the work done and the heat transfer.
Given:
m = 4500 kg/min ; P1 = 425 KPa; T1 = 1360K ; P2 = 101 KPa; PVn = C
n = 1.45 ; KE and PE are negligible
For Air: R = 0.287 KJ/kg-K; k = 1.4; Cp = 1.0045 KJ/kg-K; Cv = 0.7175 KJ/kg-K
n1
nmRT1 P2 n
W Q Δh 1
1 n P1
n1
kn P2 n
Q1); mCn (T2
T Cn Cv ; T2 T1
1 n 1 P
1.451
1.45(4500)(0.287)(1360) 101 1 33.938KW
1.45
W
60(1 1.45) 425
1.451
1.45
4500(0.7175)(1.4 - 1.45)(1360) 101 1 2926KW
Q
60(1 1.45) 425
Q 2926KW (heatis rejected)
50. Steam flows steadily through a turbine with a mass flow rate of 2.52 kg/sec. The inlet steam conditions are
7000 KPa and 500C. The exit steam pressure is 20 KPa and the expansion is isentropic. Determine the
turbine work in KW.
Q h KE PE
W Q 0 (for adiabatic)
KE andPE arenegligible
W -h -(h2 - h1 ) KJ/kg
W m(h1 - h2 ) KW
where m is themass flow rate inkg/sec
W 2.52(3410.3 2239.45) 2959.54 KW
51. In thermodynamics, a fixed quantity of mass selected for the purpose of study is called a:
a. system
b. closed system
c. open system
d. control volume
52. In order for a system to be in thermal equilibrium, which of the following properties must be the same
throughout the system?
a. mass
b. pressure
c. temperature
d. volume
53. A cycle consists of a series of processes that:
a. eventually return to the first state of the first process
b. are continually repeated
c. are always in equilibrium or quasi-equilibrium
d. none of these
54. A 0.5 m3 container is filled with a fluid whose specific volume is 0.001 m 3/kg. At standard gravitational
acceleration, the contents of this container weigh:
a. 2010 N
b. 3220 N
c. 4905 N
d. 7830 N
3
V 0.5 m
V
υ
m
0.5
m 0.001 500 kg
W 500(9.81) 4905N
55. Which temperature below is equivalent to 125 °F?
a. 52 °C
b. 125 °C
c. 602 °R
d. 315 K
F 32 125 32
C 1.8 1.8 51.7C
56. On a day when the barometer reads 755 mm Hg, a tire pressure gage reads 204 KPa. The absolute pressure
in the tire is:
a. 100 KPa
b. 204 KPa
c. 1.54 m Hg
d. 2.29 m Hg 755(101 .325 )
Pabs 204 305 KPa 2.29 m Hg
760
57. The fan pressure differential gage on an air handler reads 12 cm H2O. What is this pressure differential in Kilo
Pascals?
a. 0 kPa
b. 0.93 kPa
c. 1.18 kPa
d. 1.37 kPa
101.325
0.12 m H O x
KPa 1.18 KPa
2
10.33 cm H2O
58. At a pressure of 4 Mpa, the temperature at which liquid water boils is:
a. 29.0°C
b. 100.0°C
c. 143.6°C
d. 250.4°C
59. The specific volume of a system consisting of refrigerant 134a at 1,000 KPa is 0.01 m3/kg. The quality of the R-
134a is:
a. 12.62 %
b. 46.92 %
c. 68.32 %
d. Not applicable
At 1000 KPa (10 Bar)
L
υf 0.870
kg
L
υg 20.33
kg
10 0.870 x(20.33 0.870)
x 47%
60. A system contains water at 2,000 KPa, 220°C. The phase of this water is:
a. Liquid
b. Liquid-vapor mixture
c. Vapor
d. Solid
61. KNA thermodynamic system contains water at 10 m 3 of air whose pressure and temperature are 300 KPa,
127°C respectively. The weight for this system is:
a. 92 KN
b. 127 KN
c. 192 KN
d. 256 KN
W mg 9367.5(9.8 1)
9367.5(9.8 1) 9367.5(9.8 1) 92 KN
1000
62. Air in a closed piston-cylinder device arranged to maintain a pressure of 400 KPa is heated from 27°C to
227°C. Initially the volume of the air is 1 liter. What is the final air volume?
a. 0.5 liters
b. 0.00167 m3
c. 2.4 liters
d. 0.036 m3
V1 V2
T1 T2
0.001 V2
(27 273) (227 273)
V2 0.00167 m3
63. Propane gas (Pc = 4.26 MPa, Tc = 370 K) is maintained at 6.39 MPa and 444 K. How much volume does 1 kg
of this gas fill?
a. 8.78 liters
b. 12.3 liters
c. 13.1 liters
d. 15.7 liters
C3H8 : Propane
M 44
R 0.189 KJ
kg - K
PV mRT
1(0.189)(444)
V 0.131 m3 13.1Liters
6390
64. Air (Cp = 1.005 kJ/kg-k) is heated from 27°C to 327°C. How much does the specific internal energy of the air
change as a result of this heating?
a. 301.5 kJ/kg decrease
b. 301.5 kJ/kg increase
c. 215.4 kJ/kg decrease
d. 215.4 kJ/kg increase
Cp CV R
66. The interaction that occurs between a system and its surroundings as the system executes a process, which is
the result of the system being at a temperature different from the surroundings, is:
a. Mass transfer
b. Heat transfer
c. Work transfer
d. None of these
67. Air is expanded from 1 MPa, 327°C to 200 kPa in a closed piston-cylinder device executing a PV1.2 = constant
process. The work produced during this process is:
a. 202.6 kJ/kg
b. 263.4 kJ/kg
c. 361.7 kJ/kg
d. 422.8 kJ/kg
68. Oxygen (M = 32 kg/kg-mol) at 200 kPa, 27°C is contained in a piston-cylinder device arranged to maintain a
constant pressure. How much work is produced by this system when it is heated to 227°C?
a. 0 kJ/kg
b. 11.2 kJ/kg
c. 37.1 kJ/kg
d. 52.0 kJ/kg
8.3143 KJ
R 32 0.26
kg - K
W P(V2 V1) Isobaric (Nonflow )
KJ
W mR (T T ) 52
2 1
kg
69. A 1000 kg automobile accelerates from 10 km/hr to 120 km/hr. How much work does this require?
a. 0 kJ
b. 501 kJ
c. 552 kJ
d. 80 kJ
2
m(v2 v 2 )
1
W KJ
2(1000 )
v1 2.78 m
sec
v2 33.33 m
sec
70. Steam at 1 MPa, 300°C flows through a 30 cm diameter pipe with an average velocity of 10 m/s. The mass flow
rate of this steam is:
a. 0.731 kg/s
b. 2.74 kg/s
c. 3.18 kg/s
d. 3.78 kg/s
m ρAv 2.739 kg
sec
71. Refrigerant-134a flows through a pipe at 800 KPa, 50°C. The specific flow work required to move this fluid
through a cross-section of the pipe is:
a. 22.84 kJ/kg
b. 31.60 kJ/kg
c. 37.21 kJ/kg
d. 40.70 kJ/kg
υ 28.547 L
kg
28.547 KJ
Ef PV 800 22.84
1000 kg
72. A mixture of ideal gases has an apparent molecular weight of 36.4 kg/kg-mole and a specific enthalpy of 273.2
kJ/kg when the temperature is 127 °C. The specific internal energy of this gas mixture is:
a. 98.72 kJ/kg
8.3143
b. 153.1 kJ/kg R 0.228 KJ
c. 181.8 kJ/kg 36.4 kg
d. 273.2 kJ/kg K
h C pt
273.2 Cp (127 273)
Cp 0.683
Cp Cv R
Cv 0.683 0.228 0.445
KJ
U 0.445(127 273) 182
kg
72. A 12 V DC electrical motor draws a current of 18 amps. How much work does this motor produce over a 10 -
minute period of operation?
a. 97.42 kJ
b. 129.6 kJ
c. 216.0 kJ
d. 318.2 kJ
73. Air at 1 MPa, 27°C is contained in a piston-cylinder device that is arranged to maintain a constant pressure.
How much heat is required to raise the temperature of this air to 527°C?
a. 180 KJ/kg
b. 370 KJ/kg
c. 502 KJ/kg
d. 1040 KJ/kg
KJ
Q C (T T ) 1.0045(527 27) 502.25
p 2 1
kg
ΔU 0.7175(527 27) 358.75
W 0.287(527 27) 143.5
KJ
Q ΔU W 502.25
kg
74. Two kilograms of steam at 2 MPa, 250° C are contained in a rigid vessel. How much heat must be removed from
this vessel to cool it to 25°C?
a. 5030 kJ
b. 2512 kJ
c. -2512 kJ
d. -5030 kJ
At 2000 KPa ; t 250C
KJ
U 2679 .6
1
kg
υ1 0.11144
At 25C ; υ1 0.11144
υf 0.001003
Uf 104.88
υg 43.36
Ug 2409 .8
x2 0.0025
U2 110.75
Q -5137.7 KJ
75. Air is compressed in a piston-cylinder device. Using constant specific heats and treating the process as internally
reversible, the amount of work required to compress this air from 100 KPa, 27°C to 2000 KPa, 706°C is:
a. -298.7 kJ/kg P1 100 KPa ; T1 27 273 300 K
b. -512.2 kJ/kg
P2 2000 KPa ; T2 206 273 979 K
c. 721 kJ/kg
n 1
d. 103 kJ/kg T n
2 P
T P2
1 1
n 1.65
mR (T2 T1)
W NonFlow
1 n
KJ
W 298.71
kg
76. Air enters an adiabatic, steady-flow turbine at 1 MPa, 527° C through a 1m2 duct with a velocity of 100 m/s. The air
leaves the turbine at 100 kPa, 157C. The mass flow rate of the air is:
a. 87.4 kg/s
b. 137.3 kg/s
c. 327.2 kg/s
d. 435.34 kg/s
P
RT
ρ
m ρAv
ρ1 1000
4.36
0.287(527
273)
m 4.36(1)100 435.34 kg/sec
77. Air enters a steady state, steady-flow turbine at 1,000 KPa, 550°C through a 1m2 duct with a velocity of 100 m/s.
The air leaves this turbine at 100 KPa, 200°C through a duct of the same size. Determine the work produced by this
Turbine for an internally reversible process.
a. 107.62 MW
b. 102.67 MW
c. 106.27 MW
d. 201.71 MW
m ρAv ; A 1m2; v1 m
100 sec
kg
ρ1 P1 4.23
RT m3
1
m 423.4 kg
sec
m ρ2Av2
ρ2 P2 0.74 kg
RT2 m3
v2 574.8 m
sec
n1
T2 P2 n
T P
1 1
n 1.32
Q Δh ΔKE ΔPE W
Q mC n(T2 T1)
Cn C v k n
1 n
Δh mC p(T2 T1)
2
v2 v 2
ΔKE m 1
2(1000)
ΔPE
z2 z1
mg
1000
W 107,618.2 KW
78. Steam at 4 MPa, 400° C enters a steady-flow, adiabatic turbine through a 20 cm-diameter-pipe with a velocity of 20
m/s. It leaves this turbine at 50 kPa with a quality of 80% through a 1 m-diameter pipe. What is the velocity of the
steam as it leaves the turbine?
a. 10.3 m/s
b. 28.2 m/s
c. 32.6 m/s
d. 73.3 m/s
At P 4000 KPa ; t 400C
KJ
h 3214 .1
kg
kg
ρ 13.630
m3
KJ
U 2920 .6
kg
P 50 KPa ; x
80% h 2183 .9
ρ 0.3858
m ρAv
π kg
m 13.630 0.20 20 8.56
2
4 sec
8.56 m
v 2 28.26
π sec
0.3858
24 1
79. Saturated liquid water enters an adiabatic steady-flow throttle valve at 500 kPa and leaves at 100 kPa. What is the
quality of the water liquid-vapor mixture leaving this valve?
a. 9.87%
b. 10.6%
c. 14.3%
d. 21.1%
80. Air enters the after burner nozzle of a jet fighter at 427°C with a velocity of 100 m/s. It leaves this adiabatic nozzle
at 377°C. Assuming that the air specific heats do not change with temperature, the velocity at the nozzle exit is:
a. 142 m/s
b. 178 m/s
c. 227 m/s
d. 332 m/s
Q Δh ΔKE ΔPE W
0 Δh ΔKE 0 0
ΔKE Δh
2
V2 V 2
1
Cp (T2 T1)
2000
m
v 2 2000Cp (T1 T2 ) v 21
sec
v 2 332.34 m
sec
81. Air is compressed from 100 KPa, 300 K to 500 KPa, 500 K in a steady state, steady-flow compressor. Determine
the work required for this compressor per kg:
a. -132 kJ/kg
b. -181 kJ/kg
c. -203 kJ/kg
d. -241 kJ/kg
P1 100 KPa ; T1 300 K
P2 500 KPa ; T2 500 K
n1
T2 P2 n
T P
1 1
n 1.46
nmR (T2 T1) KJ
W 180.8 kg
1n
82. A 3 m3 drum contains a mixture at 101 KPa and 35C of 60% Methane (CH4) and 40% oxygen (O2) on a volumetric
basis. Determine the amount of oxygen that must be added at 35C to change the volumetric analysis to 50% of
each component. Determine also the new mixture pressure.
For mCH
x 4
CH 4: M = 16; k = 1.321 CH
m 4
101(3) mCH
m 2.65 kg x 4
83. Air enter the nozzle as shown at a pressure of 2700 KPa at a velocity of 30 m/sec and with an enthalpy of 923
KJ/kg, and leaves with a pressure of 700 KPa and enthalpy of 660 KJ/kg. If the heat loss is 0.96 KJ/kg, find the exit
velocity in m/sec if the mass flow rate is 0.2 kg/sec.
a. 727
b. 635
c. 842
d. 574
Q Δh ΔKE ΔPE W
For a nozzle W 0; Δz 0
2
v2 - (30)2
- 0.96 (660 - 923) 00
200
0
v2 727.2 m
sec
84. A gaseous mixture composed of 25 kg of N2, 3.6 kg of H2, and 60 kg of CO2 is at 200 KPa, 50C. Find the
respective partial pressures and compute the volume of each component at its own partial pressure and 50 C.
Given: mN2 = 25 kg ; mH2 = 3.6 kg ; mCO2 = 60 kg
m = 25 + 3.6 + 60 = 88.6 kg
xN2 = 0.282 ; xH2 = 0.041 ; xCO2 = 0.678
P = 200 KPa ; T = 323 K
xi
yi Mi
xi
Mi
xi 0.282 .041 .678
Mi 28 2 44 0.046
y N 0.219
2
y H 0.446
2
yCO 0.335
2
Pi
yi
P
PN2 = .219(200) = 43.8 KPa
PH2 = .446(200) = 89.2 KPa
PCO2 = 0.335(200) = 67 KPa
Pi Vi miRiTi
25(0.297(323)
VN2 54.76 m3
43.8
3.6(4.16)(323)
VH2 54.23 m3
89.2
60(0.189)(323)
54.67 m3
VCO2
67
85. A centrifugal pump compresses 3000 L/min of water from 98 KPa to 300 KPa. The inlet and outlet temperatures
are 25C (d = 994.36 kg/m3). The inlet and discharge piping are on the same level, but the diameter of the inlet
piping is 15 cm whereas that of the discharge piping is 10 cm. Determine the pump work in Kilowatts.
3,000 3
Q 1000(60) 0.05 m
sec
v1 0.05(4) m
π(0.15) 2.83 sec
2
v 0.05(4) m
2 2 6.4
π(0.10) sec
Q ΔU Δ(Pυ) ΔKE ΔPE W
00 300 98 2 2
(6.4) (2.83)
0W
2000
994.36
KJ
W 0.22
kg
m 0.05(994.36) 218.8 kg
sec
W 0.22(218.8 ) 48
KW
86. A closed gaseous system undergoes a reversible process in which 30 KJ of heat are rejected and the volum e
changes 0.14 m3 to 0.55 m3. The pressure is constant at 150 KPa. Determine the change of internal energy U and
the work done W.
Q ΔU W
W P(V2 V1) 150(0.55 0.14) 61.5 KJ
- 30 ΔU 61.5
ΔU -91.5 KJ
87. Air in a piston cylinder occupies 0.12 m 3 at 552 KPa. the air expands in reversible adiabatic process in which
PV1.4 = C, doing work on the piston until the volume is 0.24 m3. Determine
a) the work of the system
b) the net work if the atmospheric pressure is 101 KPa
Pr ocess : PV k C
552(0.12) 1.4 P2 (0.24)1.4
P2 209 KPa
P V P1V1
W 2 2 40.2 KJ
1- k
Wa 101(0.24 - 0.12) 12.12 KJ
wnet 40.2 - 12.12 28.08 KJ
88. A piston cylinder contains air at 600 KPa, 290 K and a volume of 0.01 m3. A constant pressure process gives 54 KJ
of work out. Determine the heat transfer of the process.
Given:
P1 = P2 = 600 KPa W P(V2 V1) mR (T2 T1)
T1 = 290 K P1V1 mRT 1
V1 = 0.01 m3 P V
m 1 1 0.07 kg
W = 54 KJ (work out) RT1
T2 W
mR T 478.4 K
1
Q mC p (T2 - T1)
Rk KJ
C
p k - 1
1.0045 kg - K
Q 13.24 KJ
89. A 0.5 m3 rigid tank containing hydrogen at 20C and 600 KPa is connected by a valve to another 0.5 m 3 rigid tank
that holds hydrogen at 30C and 150 KPa. Now the valve is opened and the system is allowed to reach thermal
equilibrium with surroundings which are at 15C. Determine the final pressure. Assume hydrogen as an ideal gas.
(For hydrogen R = 4.125 KJ/kg-K)
Given: PV
Tank A m RT
VA = 0.5 m3 mA
600(0.5)
0.25 kg
TA1 = 20 + 273 = 293 K 4.125(293)
PA1 = 600 KPa 150(0.5)
mB 0.06 kg
Tank B 4.125(303)
VB = 0.5 m3 At equilibriu m state
TB1 = 30 + 273 = 303 K
V 0.5 0.5 1m3
PB1 = 150 KPa
m 0.25 0.06 0.31 kg
0.31(4.125 )(15 273)
P 1
P 368.28 KPa
90. During some actual expansion and compression processes in piston cylinder devices, the gases have been
observed to satisfy the relationship PVn = C, where n and C are constants. Calculate the work done when a gas
expands from a state of 150 KPa and 0.03 m 3 to a final volume of 0.2 m3 for the case of n = 1.3. Also show the
process on the PV diagram.
Given:
P1 = 150 KPa ; V1= 0.03 m3 PV n C
V2 = 0.2 m 3 PVnPVnC
1 1 2 2
For a Closed system
W P dV
C
P n
V
By integratio n
2 P V P 1V 1
W PdV 2 2
1
1 nn
PVn V 0.03 1.3
P2 P1 1 150
11
V2n V2 0.2
P2 12.74 KPa
2 P2 V2 P1V1 12.74(0.2) 150(0.03)
W 1 PdV
1 1 1.3
W 6.533 KJ n
91. Five kg of methane gas is fed to a cylinder having a volume of 20 m 3 and initially containing 25 kg of methane at
a pressure of 10 bar. Determine the specific volume, in m3/kg, of the methane in the cylinder initially. Repeat for the
methane in the cylinder after the 5 kg has been added. (For Methane: R = 0.5183 KJ/kg-K; k = 1.321)
m1 = 25 kg ; V1 = 20 m3 ; P1 = 10 Bar = 1000 KPa
m2 = 25 + 5 = 30 kg
P1V1 m1RT1
V 20
υ 1 0.8 m3/kg
1
m1 25
PV
T 1 1 1000(20) 1543 .5K
1
m1R 25(0.5183 )
V2 20
υ2 0.66 m3/kg
m2 25
5
92. A vessel of volume 0.2 m3 contains nitrogen at 101.3 KPa and 15ºC. If 0.2 kg of nitrogen is now pumped into the
vessel, calculate the new pressure when the vessel has returned to its initial temperature. For nitrogen: M = 28 and
k = 1.399. (187 KPa)
8.3143
R 0.297
28
PV mRT
101.3(0.2)
m 0.297(15 273) 0.237 kg
mFinal 0.237 0.2 0.437 kg
93. A certain perfect gas of mass 0.01 kg occupies a volume of 0.003 m 3 at a pressure of 700 KPa and a temperature
of 131ºC. The gas is allowed to expand until the pressure is 100 KPa and the final volume is 0.02 m 3. Calculate:
a) the molecular weight of the gas (16)
b) the final temperature (111.5ºC)
PV mRT
700(0.003)
R 0.01(131 273) 0.52
8.3143
M 0.520 16
100(0.02)
t 0.01(0.520) 273 111.6C
94. A perfect gas has a molecular weight of 26 kg/kgmol and a value of k = 1.26. Calculate the heat rejected
a) when 1 kg of the gas in contained in a rigid vessel at 300 KPa and 315ºC, and is then cooled until the
pressure falls to 150 KPa. (-361 KJ)
8.3143
R 0.32
26
R
C 1.23
v
k1
T1 315 273 588
At V C
P1 P2
T1 T2
150(588)
T2 294
300
Q mCv (T2 T1 ) 1(1.23(294 588)
Q 361.2 KJ (rejected)
b) when 1 kg/sec mass flow rate of the gas enter a pipeline at 280ºC and flows steadily to the end of the
pipe where the temperature is 20ºC. Neglect changes in kinetic and potential energies.(-403 KW)
Q Δh ΔKE ΔPE W
Q Δh 0 0 0
Δh mC P (T2 T1)
CP Rk
k1
8.3143
R 0.320 KJ
26 kg - K
CP Rk KJ
k 1.550 kg - K
1
Q Δh 1(1.550)(20 - 280) 403.2 KW
93. The mass analysis of hydrocarbon fuel A is 88.5% Carbon and 11.5% Hydrogen. Another hydrocarbon fuel B
requires 6% more air than fuel A for complete combustion. Calculate the mass analysis of Fuel B.
Solution:
Fuel A: C = 0.885 ; H = 0.115
Fuel B: C = ; H =
(A/F)B = 1.06(A/F)A
(A/F)A = 11.44(0.885) + 34.32(0.115) = 14.0712 kg/kg
(A/F)B = 1.06(14.0712)= 14.9155 kg/kg
For fuel B: H + C = 1
H = (1 – C)
14.9155 = 11.44C + 34.32(1-C)
C = 84.8%
H = 15.2%
94. A diesel engine uses a hydrocarbon fuel represented by C12H26 and is burned with 30% excess air. The air and fuel
is supplied at 1 atm and 25C. Determine
a. the actual air-fuel Ratio
b. the m3 of CO2 formed per kg of fuel if the product temp. is 400C and a pressure of 1 atm.
c. The M and R of the Products
d. The M and R of the dry flue gas
Combustion with 100% theoretical air (basis 1 mole of fuel)
C12H26 + aO2 + a(3.76)N2 bCO2 + cH2O + a(3.76)N2
a = 18.5
b = 12
c = 13
Combustion with 30% excess air
C12H26 + 1.30aO2 + 1.30a(3.76)N2 bCO=+ cH2O + dO2 + 1.30a(3.76)N=
d = 5.55
nP = b + c + d + 1.3(18.5)(3.76) = 120.978
97. When a certain perfect gas is heated at constant pressure from 15ºC to 95ºC, the heat required is 1136 KJ/kg.
When the same gas is heated at constant volume between the same temperatures the heat required is 808 KJ/kg.
Calculate Cp, Cv, k, and M of the gas. (14.2 KJ/kg; 10.1 KJ/kg; 1.405; 4.1 and 2.208)
98. A quantity of a certain perfect gas is compressed from an initial state of 0.085 m 3, 100 KPa to a final state of 0.034
m3, 390 KPa. the Cv = 0.724 KJ/kg-ºC and Cp = 1.020 KJ/kg-ºC. The observed temperature rise is 146ºK. Calculate
R, the mass present, and U of the gas.(0.296 KJ/kg-K; 0.11 kg; 11.63 KJ)
99. A mass of 0.05 kg of air is heated at constant pressure of 200 KPa until the volume occupied is 0.0658 m 3.
Calculate the heat supplied, the work and the change in entropy for the process if the initial temperature is 130ºC.
(Q = 25.83 KJ; W = 7.38 KJ)
100.A 1 kg of nitrogen is compressed reversibly and isothermally from 101 KPa, 20ºC to 420 KPa. Calculate the nonflow
work and the heat flow during the process assuming nitrogen to be a perfect gas. ( Q = W = 124 kJ/KG)
101.Air at 102 KPa, 22ºC, initially occupying a cylinder volume of 0.015 m 3 is compressed isentropically by a piston to a
pressure of 680 KPa. Calculate the final temperature, the final volume, the work done on the mass of air in the
cylinder. (234.3 ºC; .00387 m3; 2.76 KJ)
102.1 kg of air is compressed from 110 KPa, 27 ºC in a polytropic process where n = 1.3 until the final pressure is 660
KPa. Calculate:
a) ∫PdV
b) - ∫VdP
c) S
103. There are 1.36 kg of air at 138 KPa stirred with internal paddles in an insulated rigid container, whose volume is
0.142 m3until the pressure becomes 689.5 KPa. Determine the work input and PV. ( 196.2 KJ; 78.3 KJ)
104. During an isentropic process of 1.36 kg/sec of air, the temperature increases from 4.44ºC to 115.6 ºC. for a
nonflow process and for a steady flow process (KE = 0 and PE = 0) Find:
a) U in KW
b) H in KW
c) W in KW
d) S in KW/ºK
e) Q in KW
105. A certain perfect gas is compressed reversibly from 100 KPa, 17 ºC to a pressure of 500 KPa in a perfectly
thermally insulated cylinder, the final temperature being 77 ºC. The work done on the gas during the compression
is 45 KJ/kg. Calculate, k , Cv, R and M of the gas.( 1.132; 0.75 KJ/kg-ºK; 0.099 KJ/kg-ºK; 84)
106. 1 kg of air at 102 KPa, 20 ºC is compressed reversibly according to a law PV 1.3 = C to a pressure of 550 KPa.
Calculate the work done on the air and the heat supplied during the compression. (133.46 KJ/kg; -33.3 KJ/kg)
107. Oxygen (M = 32) is compressed polytropically in a cylinder from 105 KPa, 15ºC to 420 KPa in such a way that
one third of the work input is rejected as heat to the cylinder walls. Calculate the final temperature of the oxygen.
Assume oxygen to be perfect gas and take Cv = 0.649 KJ/kg-K. (113 ºC)
108. Air at 690 KPa, 260ºC is throttled to 550 KPa before expanding through the nozzle to a pressure of 110 KPa.
Assuming that the air flows reversibly in steady flow through the nozzle and that no heat is rejected, calculate the
velocity of the air at exit from the nozzle when the inlet velocity is 100 m/sec. ( 636 m/sec)
109. Air at 40ºC enters a mixing chamber at a rate of 225 kg/sec where it mixes with air at 15ºC entering at a rate of
540 kg/sec. Calculate The temperature of the air leaving the chamber, assuming steady flow conditions. Assume
that the heat loss is negligible. (22.4ºC)
A heat engine has a thermal efficiency of 45%. How much power does the engine produce when heat is transferred into
it at a rate of 109 kJ/Hr?
A) 50 MW
B) 75 MW
C) 100 MW
D) 125 MW
A refrigerator has a coefficient of performance of 1.6. How much work must be supplied to this refrigerator for it to reject
1000 kJ of heat?
A) 385 kJ
B) 627 kJ
C) 836 kJ
D) 1000 kJ
The thermodynamic efficiency of a heat engine that rejects heat at a rate of 20 MW when heat is supplied to it at a rate
of 60 MW is:
A) 33.3%
B) 50%
C) 66.7%
D) 75%
A Carnot engine operates using a 527 °C energy reservoir and a 27 °C energy reservoir. The thermodynamic efficiency
of this engine is:
A) 50%
B) 62.5%
C) 73.6%
D) 103%
A Carnot heat pump uses thermal reservoirs at -27 °C and 57 °C. How much power does this pump consume to produce
a 100 kW heating effect?
A) 9.1 kW
B) 12.7 kW
C) 15.3 kW
D) 20.7 kW
Saturated water vapor at 150 kPa is condensed to saturated liquid in a steady -flow, isobaric heat exchanger. The
released heat is transferred to the surrounding air whose temperature is 20 °C. The increase of the entropy associated
with this process is:
A) -4.731 kJ/kg-K
B) -2.366 kJ/kg-K
C) 2.366 kJ/kg-K
D) 4.731 kJ/kg-K
Steam at 2 MPa, 300 °C is expanded in a steady-flow, adiabatic turbine to 30 kPa. What is the lowest possible
temperature at the outlet of this turbine?
A) 69.1 °C
B) 101.1 °C
C) 150.7 °C
D) 203.2 °C
Steam at 2 MPa, 300 °C is expanded through a steady-flow, adiabatic turbine to 30 kPa. How much work does this
turbine produce?
A) 478.7 kJ/kg
B) 523.2 kJ/kg
C) 639.2 kJ/kg
D) 741.6 kJ/kg
Air at 5 MPa, 967 °C is expanded through a steady-flow device to 100 kPa, 27 °C. What is the change in the specific
entropy of the air?
A) -1.372 kJ/kg-K
B) -0.269 kJ/kg-K
C) 1.742 kJ/kg-K
D) 2.638 kJ/kg-K
A 0.5-kg steel (C = 0.5 kJ/kg-k) rivet cools from 800 K to 300 K upon being installed in a riveted building structure. The
entropy change of this rivet is:
A) -0.631 kJ/K
B) -0.245 kJ/K
C) 0.245kJ/K
D) 0.631 kJ/K
Oxygen at 100 kPa, 27 °C is compressed to 1 MPa in an adiabatic compressor whose isentropic efficiency is 0.80. The
oxygen temperature at the compressor outlet is:
A) 376 K
B) 421 K
C) 566 K
D) 649 K
Water undergoes the reversible process illustrated here as it passes through a steady -flow device that has one outlet
and one outlet. How much work does this device produce?
A) 0 kJ/kg
B) P (v2 - v1) kJ/kg
C) R (T2 - T1) kJ/kg
D) cv (T2 - T1) kJ/kg
Air is expanded in a closed system from 1 MPa, 327 °C to 100 kPa in an isentropic process. The system surroundings
are at 100 kPa, 27 °C. How much useful work did this system produce during this process?
A) 91 kJ/kg
B) 103 kJ/kg
C) 135 kJ/kg
D) 210 kJ/kg
A 1 m3 vessel contains air at 1 MPa, 327 °C. Assuming standard conditions for the surroundings, what is the maximum
amount of work that can be done by the air in this vessel?
A) 790 kJ
B) 826 kJ
C) 1012 kJ
D) 1290 kJ
Steam enters a turbine at 3 MPa, 350 °C with a velocity of 15 m/s. What is the specific exergy of this steam assuming
the surroundings are at standard conditions?
A) 678 kJ/kg
B) 827 kJ/kg
C) 968 kJ/kg
D) 1116 kJ/kg
Steam at 3 MPa, 350 °C is expanded through an adiabatic, steady-flow turbine to a saturated vapor at 100 kPa. The
second law efficiency of this turbine is:
A) 48.2%
B) 63.7%
C) 70.7%
D) 82.1%
A heat exchanger maintains the air temperature in a room at 25 °C by condensing saturated water vapor at 125 kPa to
saturated liquid water. The specific exergy destruction associated with this heat exchanger is:
A) 932 kJ/kg
B) 958 kJ/kg
C) 1241 kJ/kg
D) 1378 kJ/kg
Air is compressed from 100 kPa, 27 °C to 900 kPa, 327 °C in an adiabatic piston-cylinder device. What is the
irreversibility of this process?
A) 19.66 kJ/kg
B) 22.31 kJ/kg
C) 28.73 kJ/kg
D) 32.17 kJ/kg
An adiabatic, steady-flow heat exchanger condenses 10,000 kg/hr of saturated steam vapor at 200 kPa to a saturated
liquid also at 200 kPa. The condensing steam heats 220,000 kg/hr of air at 100 kPa, 25 °C to 100 kPa, 125 °C. What is
the rate at which exergy is destroyed by this heat exchanger?
A) 0 MJ/hr
B) 270 MJ/hr
C) 1327 MJ/hr
D) 2295 MJ/hr
A Carnot vapor power cycle operates its boiler at 3.0 MPa and its condenser at 50 kPa. What is the thermal efficiency
of this cycle?
A) 20%
B) 30%
C) 40%
D) 50%
A simple Rankine cycle operates the boiler at 3 MPa with an outlet temperature of 350 °C and the condenser at 50 kPa.
Assuming ideal operation and processes, what is the thermal efficiency of this cycle?
A) 7.7%
B) 17.7%
C) 27.7%
D) 37.7%
A simple Rankine cycle operates its boiler at 3 MPa with an outlet temperature of 350 °C and its condenser at 50 kPa.
The turbine has an isentropic efficiency of 0.9 while all other operating conditions and process are ideal. What is the
thermal efficiency of this cycle?
A) 25.0%
B) 30.9%
C) 35.9%
D) 40.9%
A simple, ideal Rankine cycle operates the boiler at 3 MPa and the condenser at 50 kPa. The temperature at the boiler
outlet is 400 °C. What is the rate at which heat must be supplied to the water in the boiler for a power production of 100
MW?
A) 157 MW
B) 218 MW
C) 273 MW
D) 352 MW
An ideal Rankine cycle with reheat operates the boiler at 3 MPa, the reheater at 1 MPa, and the condenser at 50 kPa.
The temperature at the boiler and reheater outlets is 350 °C. What is the thermal efficiency of this cycle?
A) 24.5%
B) 26.5%
C) 28.5%
D) 30.5%
An ideal Rankine cycle with reheat operates the boiler at 3 MPa, the reheater at 1 MPa, and the condenser at 50 kPa.
The temperature at the boiler and reheater outlets is 350 °C. The boiler and reheater are fired with a fuel that releases
9,000 kJ/kg of heat as it is burned. What is the mass flow rate of the fuel for such a cycle when sized to produce 50
MW of net work?
A) 40 Mg/hr
B) 50 Mg/hr
C) 60 Mg/hr
D) 70 Mg/hr
An ideal Rankine cycle with an open-feedwater-heater regenerator operates the boiler at 3 MPa, the regenerator at 125
kPa, and the condenser at 50 kPa. At the boiler outlet, the temperature is 350 °C. What percentage of the mass flow
rate passing through the boiler is bled from the turbine for the regenerator?
A) 4.85%
B) 7.31%
C) 10.6%
D) 13.2%
An ideal Rankine cycle with an open-feedwater-heater regenerator operates the boiler at 3 MPa, the regenerator at 125
kPa, and the condenser at 50 kPa. At the boiler outlet, the temperature is 350 °C. What is the thermal efficiency of this
cycle?
A) 24.6%
B) 28.6%
C) 32.6%
D) 36.6%
A simple Rankine cycle operates the boiler at 3 MPa and the condenser at 50 kPa. The temperature at the boiler outlet
is 350 °C. The energy source is at 400 °C and the energy sink is at 27 °C. What is the irreversibility of this cycle per unit
of mass passing through the boiler?
A) 561.2 kJ/kg
B) 613.4 kJ/kg
C) 694.2 kJ/kg
D) 767.8 kJ/kg
A simple Rankine cycle produces 40 MW of power, 50 MW of process heat and rejects 60 MW of heat to the
surroundings. What is the utilization factor of this cogeneration cycle neglecting the pump work?
A) 50%
B) 60%
C) 70%
D) 80%
A basic R-134a, ideal vapor-compression refrigerator operates its evaporator at -16 °C and its evaporator at 1.4 MPa.
How much power will the compressor require to service a 10 kW cooling load?
A) 4.03 kW
B) 5.97 kW
C) 7.32 kW
D) 10.0 kW
A basic R-134a, ideal vapor-compression refrigerator operates its evaporator at 157 kPa and its evaporator at 1.4 MPa.
What is the rate at which the condenser rejects heat when this refrigerator services a 100 kW load?
A) 80 kW
B) 103 kW
C) 120 kW
D) 141 kW
An ideal R-134a vapor-compression heat pump operates its evaporator at 1.4 MPa and its condenser at -16 °C. The
coefficient of performance of this heat pump is:
A) 2.48
B) 2.79
C) 3.43
D) 3.79
A R-134a vapor-compression refrigerator operates its evaporator at 1.4 MPa and its condenser at 157 kPa. All the cycle
states and processes are ideal except for the compressor, which has an isentropic efficiency of 79%. How much power
must be supplied to the compressor when this refrigerator serves a100 kW cooling load?
A) 27.3 kW
B) 34.2 kW
C) 52.0 kW
D) 100 kW
A simple R-134a vapor-compression refrigerator system operates its evaporator at 157 kPa and the exit of the
compressor at 1.4 MPa. The working fluid enters the throttle valve as a saturated liquid at 1.2 MPa as a result of
pressure losses in the condenser and connection lines. What is the coefficient of performance of this device?
A) 2.64
B) 2.93
C) 3.26
D) 3.69
An ideal R-134a, dual compressor vapor-compression refrigerator system uses a flash chamber to separate the vapor
in the evaporator feed line. This system operates the evaporator at 133 kPa, the flash chamber at 400 kPa, and the
condenser at 1.4 MPa. What fraction of the mass flow rate passing through the evaporator passes through the
condenser?
A) 0.80
B) 1.00
C) 1.20
D) 1.50
An ideal R-134a, dual compressor vapor-compression refrigerator system uses a flash chamber to separate the vapor
in the evaporator feed line. This system operates the evaporator at 133 kPa, the flash chamber at 400 kPa, and the
condenser at 1.4 MPa. What is the coefficient of performance of this device?
A) 1.87
B) 2.63
C) 2.95
D) 3.17
A simple, ideal reversible Brayton cycle uses air as the working fluid and has a pressure ratio of 6. What is the refrigerato
r COP of this cycle when the temperature at the compressor entrance is -13 °C and that at the turbine entrance is 37
°C?
A) 0.33
B) 0.72
C) 1.48
D) 1.97
The composition of a mixture of nitrogen and carbon dioxide gases is 30%-N2 and 70%-CO2 by mole fraction. What is
the mass fraction of the nitrogen constituent?
A) 15.2%
B) 21.4%
C) 30.2%
D) 63.7%
A mixture of helium and nitrogen is 50%-He and 50%-N2 by mass analysis. What is the mole fraction of the helium in
this mixture?
A) 39.7%
B) 43.2%
C) 67.2%
D) 87.5%
The composition of a gas mixture is 40%-O2, 40%-N2, and 20%-He by mass analysis. What is the apparent molecular
weight of this mixture?
A) 6.71 kg/kg-mol
B) 13.02 kg/kg-mol
C) 15.70 kg/kg-mol
D) 18.60 kg/kg-mol
The composition of a mixture of gases is 50%-CO2, 40%-O2, and 10%-He by volume analysis. What is the apparent
molecular weight of this mixture?
A) 19.3 kg/kg-mol
B) 24.6 kg/kg-mol
C) 28.7 kg/kg-mol
D) 35.2 kg/kg-mol
A 1 m3 container contains a mixture of gases composed of 0.02 kg-mol of O2 and 0.04 kg-mol of He at a pressure of
200 kPa. What is the temperature of this ideal gas mixture?
A) 300 K
B) 350 K
C) 400 K
D) 450 K
A 200 liter container holds 0.5 kg of air and 0.2 kg of helium at a temperature of 350 K. What is the pressure of this ideal
gas mixture?
A) 1.4 MPa
B) 1.6 MPa
C) 1.8 MPa
D) 2.0 MPa
A mixture composed of 70%-CO2 and 30%-He by volume analysis is contained at 1 MPa. What is the partial pressur e
of the He in this mixture?
A) 300 kPa
B) 450 kPa
C) 600 kPa
D) 700 kPa
A mixture of 30%-Ar and 70%-CO2 by volume analysis. This mixture is contained in a rigid vessel at 200 kPa, 27 °C.
The vessel is now heated until the mixture temperature is 127 °C. Assuming that the specific heats do not change, how
much heat was required?
A) 1.10 MJ/kg-mol
B) 2.40 MJ/kg-mol
C) 1.10 MJ/kg
D) 2.40 MJ/kg
A mixture consists of 30%-Ar and 70%-CO2 by volume analysis. This mixture is contained in a rigid vessel at 200 kPa,
27 oC. The vessel is now heated until the mixture temperature is 127 oC. Assuming constant specific heats, what is the
change in the entropy of the mixture?
A) 4.780 kJ/kg-mol-K
B) 6.900 kJ/kg-mol-K
C) 4.780 kJ/kg-mol-K
D) 6.900 kJ/kg-mol-K
A mixture of 20%-CO2 and 80%-N2 by volume is expanded from 1 MPa, 227 °C to 200 kPa as it passes through an
adiabatic, steady-flow turbine. Assuming this process is reversible and the specific heats are constant, how much work
is produced by this expansion?
A) 137.9 kJ/kg
B) 164.5 kJ/kg
C) 174.3 kJ/kg
D) 194.2 kJ/kg
What is the specific humidity of air at 150 kPa whose dry bulb temperature is 20 °C and relative humidity is 70%?
A) 0.000981 kg-wv/kg-da
B) 0.00382 kg-wv/kg-da
C) 0.00514 kg-wv/kg-da
D) 0.00686 kg-wv/kg-da
Using saturated liquid water and 0 °C as the reference state, what is the specific enthalpy of humid air at 120 kPa, 20
°C, and 50% relative humidity?
A) 32.71 kJ/kg-da
B) 35.63 kJ/kg-da
C) 38.93 kJ/kg-da
D) 41.72 kJ/kg-da
What is the dew-point temperature of humid air at 200 kPa, 30 °C, and 55% relative humidity?
A) 10 °C
B) 15 °C
C) 20 °C
D) 25 °C
Humid air at 150 kPa, 30 °C, and 80% relative humidity undergoes an isobaric cooling process until its temperature is
25 °C. Will any liquid condensate form during this process?
A) Yes
B) No
C) Not applicable
D) Not applicable
Humid air is cooled, dehumidified and reheated during an isobaric process. Which one of the psychometric charts
below correctly depicts these processes?
A) a
B) b
C) c
D) d
One-hundred cubic meters per minute of humid air at 101 kPa, 35 °C, 40% relative humidity is cooled to 25 °C in a
constant pressure process. The cooling rate for this process is:
A) 9.3 kW
B) 17.8 kW
C) 20.2 kW
D) 22.3 kW
Saturated humid air at 101 kPa, 20 °C is heated to 35 °C during an isobaric process. What is the final relative humidity
of this air?
A) 42%
B) 53%
C) 68%
D) 75%
Humid air at 101 kPa, 35 °C, 80% relative humidity is conditioned to 101 kPa, 25 °C, 50% relative humidity. How much
condensate is formed during this process?
A) 0.0087 kg/kg-da
B) 0.0168 kg/kg-da
C) 0.0193 kg/kg-da
D) 0.0231 kg/kg-da
Humid air at 101 kPa, 35 °C, 80% relative humidity is conditioned to 101 kPa, 25 °C, 50% relative humidity. How much
heat must be removed to accomplish this when the condensate leaves the system at 25 °C?
A) 41.7 kJ/kg-da
B) 46.7 kJ/kg-da
C) 52.3 kJ/kg-da
D) 57.5 kJ/kg-da
A standard atmospheric pressure cooling tower uses humid air at 30 °C, 60% relative humidity to cool liquid water from
55 °C to 40 °C. Saturated humid air leaves this tower at 35 °C. How much make-up water must be supplied to this
tower?
A) 0.0206 kg/kg-da
B) 0.0313 kg/kg-da
C) 0.0347 kg/kg-da
D) 0.0404 kg/kg-da
Five kilogram-mol of octane are burned with a stiochiometric amount of air. How much water is formed in the products
if the combustion is complete?
A) 15 kg-mol
B) 25 kg-mol
C) 35 kg-mol
D) 45 kg-mol
Methyl alcohol is burned with 30% excess air. How much unburned oxygen will there be in the products if the
combustion is complete?
A) 0.35 kg-mol-o2/kg-mol-fuel
B) 0.45 kg-mol-o2/kg-mol-fuel
C) 0.55 kg-mol-o2/kg-mol-fuel
D) 0.65 kg-mol-o2/kg-mol-fuel
Gaseous methane fuel is burned with 100% excess air. This combustion is incomplete with 10% of the carbon in the
fuel forming CO. The products of combustion are at 100 kPa. What is the partial pressure of the CO in the products?
A) 0.51 kPa
B) 1.36 kPa
C) 2.78 kPa
D) 10.5 kPa
Gaseous methane fuel is burned with 50% excess air. When the temperature of the products is 30 °C and the pressure
is 100 kPa, what fraction of the water in the products is liquid?
A) 31%
B) 48%
C) 62%
D) 74%
Dodecane is burned at constant pressure with 150% excess air. What is the air-fuel ratio for this process?
A) 37.5
B) 42.3
C) 48.7
D) 51.3
Liquid octane fuel is burned in an isobaric, steady-flow burner with 80% excess air. The air and fuel enter the burner at
25 °C and the combustion products leave at 427 °C. How much heat is released by this burner when the combustion is
complete?
A) 18,530 kJ/kg-fuel
B) 31,800 kJ/kg-fuel
C) 38,460 kJ/kg-fuel
D) 42,610 kJ/kg-fuel
One gallon of gasoline (octane) has a mass of 2.66 kg. What is the maximum amount of heat that can be produced
when one gallon of gasoline is burned with air?
A) 17,320 kJ/gal
B) 111,270 kJ/gal
C) 116,320 kJ/gal
D) 127,650 kJ/gal
In a metallurgical process, methane is burned at constant pressure, with a stiochiometric amount of air both of which
are at 25 °C. What is the maximum temperature of the products?
A) 1930 K
B) 2320 K
C) 2890 K
D) 3170 K
How irreversible is the combustion of methane at standard atmospheric pressure with 20% excess air when all reactants
and products are at 25 °C and the water in the products is all liquid?
A) 630,000 kJ/kg-mol-CH4
B) 780,200 kJ/kg-mol-CH4
C) 884,700 kJ/kg-mol-CH4
D) 1,110,000 kJ/kg-mol-CH4
What is the reversible work for CH4 burned with stiochiometric air when all products and reactants are at the standard
referance state?
A) 673,500 kJ/kg-mol-fuel
B) 718,300 kJ/kg-mol-fuel
C) 793,000 kJ/kg-mol-fuel
D) 817,900 kJ/kg-mol-fuel
At what temperature will 20% of carbon dioxide disassociate to carbon monoxide when the pressure is 0.1 atm?
A) 2240 K
B) 2420 K
C) 2690 K
D) 3120 K
Excess air is used in combustion reactions to control flame temperatures. Excess air will also ___ _
when Dn is positive.
A) Produce more incomplete combustion
B) Produce more complete combustion
C) Produce undesirable combustion
D) Have no effect
A mixture of 1 kg-mol of CO and 1 kg-mol of O2 is heated to 3000 K at a pressure of 1 atm. What fraction of the original
CO becomes CO2?
A) 27.8%
B) 37.6%
C) 69.2%
D) 90.1%
A mixture consists of 1 kg-mol of CO, 1 kg-mol of O2, and 2 kg-mol of N2. Treating the nitrogen as an inert gas, how
much CO2 is formed when the temperature and pressure of this mixture is 2600 K and 1 atm?
A) 0.371 kg-mol
B) 0.615 kg-mol
C) 0.832
D) 0.957 kg-mol
A mixture of 1 kg-mol of CO2, 1 kg-mol of O2, and 2 kg-mol of N2 is heated to 4000 K at a pressure of 1 atm. Assuming
that the final mixture consists of CO2, CO, O2, O, and N2, how much atomic oxygen is present in the final mixture?
A) 0.33
B) 0.50
C) 0.67
D) 0.90
What is the approximate heat of reaction at 3400 K for the disassociation of CO2 to CO?
A) 5961 kJ/kg-mol
B) 7482 kJ/kg-mol
C) 8785 kJ/kg-mol
D) 9213 kJ/kg-mol
A system is composed of gasoline liquid and vapor, and air. According to Gibbs phase rule how many independent
properties are required for phase equilibrium?
A) 0
B) 1
C) 2
D) 3
When the water temperature of the Great Salt Lake is 20 °C, what is the mass fraction of the salt dissolved in the
water? A) 26.5%
B) 32.1%
C) 36.7%
D) 40.3%
The contents of a can of soft drink consists of CO2 dissolved in water and a vapor space filled with CO2 and H2O vapor.
At 17 oC and 2 atm, what is the mole fraction of the CO2 in the liquid mixture?
A) 0.00156
B) 0.00735
C) 0.0107
D) 0.0312
At one location in a nozzle, the air temperature is 400 K and the air velocity is 400 m/s. What is the stagnation enthalpy
(based on temperature dependent specific heats) of the air at this location?
A) 300 kJ/kg
B) 357 kJ/kg
C) 470 kJ/kg
D) 481 kJ/kg
At one location in a nozzle, the air temperature is 400 K and the air velocity is 450 m/s. What is the Mach number at this
location?
A) 0.97
B) 1.12
C) 1.37
D) 2.02
Air at 20 kPa flows with a Mach number of 1.5. What is the stagnation pressure of this air?
A) 22.2 kPa
B) 41.7 kPa
C) 56.2 kPa
D) 73.4 kPa
Air in a large tank at 350 K and 200 kPa is supplied to an isentropic converging-diverging nozzle. What is the
temperature at a point in this nozzle where the Mach number is 1.2?
A) 198 K
B) 271 K
C) 360 K
D) 395 K
An isentropic, converging-diverging nozzle operates with stagnation conditions 400 kPa, 500 K. This nozzle has a throat
area of 0.01 m2 and is chocked. What is the mass flow rate through this nozzle?
A) 5.01 kg/s
B) 7.23 kg/s
C) 8.32 kg/s
D) 9.81 kg/s
The exit of the diverging section of an isentropic nozzle has twice the area of the nozzle throat. What is the Mach
number at the exit when the exit flow is supersonic?
A) 1.80
B) 2.00
C) 2.20
D) 2.40
The exit of the diverging section of an isentropic nozzle has twice the area of the nozzle throat. If the stagnation pressure
at the throat is 200 kPa, what is the pressure at the nozzle exit when the exit flow is supersonic?
A) 18.7 kPa
B) 32.2 kPa
C) 87.3 kPa
D) 137.2 kPa
An aircraft flies through 80 kPa, 270 K still air with a Mach number of 1.30. A normal shock wave will form directly in
front of this aircraft. What is the stagnation pressure acting on this aircraft?
A) 61 kPa
B) 73 kPa
C) 101 kPa
D) 193 kPa
A normal shock wave forms in the diverging portion of a nozzle at a point where Mx = 1.5. The area at the exit of this
nozzle is 50% larger then that where the shock wave forms. What is the Mach number at the nozzle exit?
A) 1.2
B) 1.12
C) 0.38
D) 0.24
Steam at 3.0 MPa, 500 °C, and negligible velocity is expanded to 0.8 MPa through an isentropic nozzle. What is the
velocity of the steam at the nozzle exit?
A) 268 m/s
B) 522 m/s
C) 738 m/s
D) 894 m/s
b. A gaseous mixture has the following volumetric analysis O2, 30%; CO2, 40% N2, 30%. Determine
a) the analysis on a mass basis
b) the partial pressure of each component if the total pressure is 100 KPa and the temperature is 32 C
c) the molecular weight and gas constant of the mixture
Gas yi M k Cp Cv R xi Pi Mixture
O2 0.30 32 1.395 0.918 0.658 0.260 0.27 30 M 35.6
CO2 0.40 44 1.288 0.845 0.656 189 0.494 40 R .234
N2 0.30 28 1.399 1.041 0.744 0.297 0.236 30 P 100
69. Consider 2 kg of CO and 1 kg of CH4 at 32C that are in a 0.6 m3 rigid drum. Find:
a) the mixture pressure P in KPa
b) the volumetric analysis
c) the partial pressures in KPa
d) the heat to cause a temperature rise of 50C.
70. A gaseous mixture has the following volumetric analysisO2, 30%; CO2, 40% N2, 30%. Determine
a) the analysis on a mass basis
b) the partial pressure of each component if the total pressure is 100 KPa and the temperature is 32 C
c) the molecular weight and gas constant of the mixture
71. A gaseous mixture has the following analysis on a mass basis, CO2, 30%; SO2, 30%; He, 20% and N2, 20%.
For a total pressure and temperature of 101 KPa and 300 K, Determine
a) the volumetric or molal analysis
b) the component partial pressure
c) the mixture gas constant
d) the mixture specific heats
72. A cubical tank 1 m on a side, contains a mixture of 1.8 kg of nitrogen and 2.8 kg of an unknown gas. The
mixture pressure and temperature are 290 KPa and 340 K. Determine
a) Molecular weight and gas constant of the unknown gas
b) the volumetric analysis
73. A mixture of ideal gases at 30C and 200 KPa is composed of 0.20 kg CO2, 0.75 kg N2, and 0.05 kg He.
Determine the mixture volume.
74. In determining the specific heat of a new metal alloy,0.15 kg of the substance is heated to 400C and then
placed in a 0.2 kg aluminum calorimeter cup containing 0.4 kg of water at 10C. If the final temperature of the
mixture is 30.5C, what is the specific heat of the alloy.( ignore the calorimeter stirrer and thermometer)
CpAl = 0.92 KJ/kg-C; Cpw = 4.186 KJ\kg-C
75. An air compressor handles 8.5 m3/min of air with = 1.26 kg/m3 and P = 101.325 KPa and it discharges at P =
445 KPag with = 4.86 kg/m3. The U = 82 KJ/kg and the heat loss by cooling is 24 KJ/kg. Neglecting KE
and PE, find W in KJ/min.
76. A 0.1 kg of aluminum (Cp=0.92 KJ/kg-C) at 90C is immersed in 1 kg of water from 20C . Assuming no heat
is lost to the surroundings or container , what is the temperature of the metal and water when they reached
thermal equilibrium?
77. Water is flowing in a pipe with varying cross section area, and at all points the water completely fills the pipe. At
point 1 the cross section area of the pipe is 0.070 m2 and the velocity is 3.50 m/sec.
a. What is the fluid speed at points in the pipe where th cross section area is 0.105 m 2 and 0.047 m2.
b. Calculate the volume of water discharged from the open end of the pipe in 1 hour.
78. A sealed tank containing sea water to a height of 11 m also contains air above the water at a gage pressure of
3 atmosphere. Water flows out from the bottom through a small hole. Calculate the efflux speed of the water.
79. A copper pot with a mass of 0.500 kg contains 0.170 kg of water at a temperature of 20C. A 0.250 kg block of
iron at 85C is dropped into the pot. Find the final temperature, assuming no heat loss to the surroundings.
Ccopper = 0.390 KJ/kg-C; Cwater = 4.19 KJ/kg-C and Ciron = 0.470 KJ/kg-C.
80. At one point in a pipeline the water speed is 3 m/sec and the gage pressure is 50 KPa. Find the gage pressure
at a second point in the line, 11 m lower than the first , if the pipe diameter at the second point is one half the
first.
81. A closed system containing a gas expands slowly in a piston cylinder in accordance to PV 2 = C. If the initial
pressure is 500 KPa, initial volume is 50 L and the final pressure is 200 KPa, find the work done by the system.
82. A steam turbine receives superheated steam at 1.4 MPa and 400C (h = 3121 KJ/kg). The steam leaves the
turbine at 0.101 MPa and 100C (h = 2676 KJ/kg).The steam enters the turbine at 15 m/sec and exits at 60
m/sec. The elevation difference between entry and exit ports is negligible. The heat loss through the turbine
walls is 2 KW. Calculate the power output if the mass flow through the turbine is 0.5 kg/sec.
83. A small circular hole 6 mm in diameter is cut in the side of a large water tank 14 m below the water level in the
tank. The top of the tank is open to the atmosphere. Find the velocity of water exiting the hole and the volum e
discharged per unit time.
84. Oxygen (M = 32) is compressed polytropically in a cylinder from 105 KPa, 15ºC to 420 KPa
The decrease in internal energy of 1.36 kg of an ideal gas is –342.9 KJ when the pressure decreases from
689.3 KPa to 137.86 KPa and the volume increases from 0.0425 m3 0.127 m3. Cv = 1.047 KJ/kg-K.
Determine the value of k.
85. The working fluid of a gas turbine passes through the machine at a steady rate of 10 kg/sec. It enters with a
velocity of 100 m/sec and specific enthalpy of 2000 KJ/kg and leaves at 50 m/sec with a specific enthalpy of
1500 KJ/kg. If the heat lost to surroundings as the fluid passes through the turbine is 40 KJ/kg, calculate the
power developed.
86. 0.07 m3 of gas at 4.14 MPa is expanded in an engine cylinder and the pressure at the end of expansion is
310 KPa. If the expansion is polytropic with PV1.35 = C, find the final volume.
87. Helium gas ( R=2.077 KJ/kg-K; k= 1.667) enters a steady state – steady flow expander at 800 KPa, 300C and
exits at 120 KPa. The mass flow rate is 0.2 kg/sec and the expansion process is PV1.3 = C. Calculate W of the
expander in KW.
88. A pressure gage at elevation 8 m on a side of a tank containing a liquid reads 57.4 KPa. Another gage at
elevation 5 m reads 80 KPa. Determine the density of the liquid.
89. Gas at a pressure of 95 KPa, volume 0.2 cu.m. and temperature 17C, is compressed until the pressure is
275 KPa and the volume is 0.085 cu.m.. Calculate the final temperature.
90. A liquid of density 800 kg/cu.m., specific heat of 2.5 KJ/kg-K and temperature of 27C is mixed with another
liquid of density 820 kg/cu.m., specific heat 1.9 KJ/kg-K and temperature of 55C in the ratio of one of the first
liquid to three of the second by volume. Find the resulting temperature.
91. A rigid container contains 1 mole of nitrogen gas that slowly receives 3 KCal of heat. What is the change in
internal energy of the gas in KJ.For N2: M = 28; K = 1.399
92. A certain perfect gas of mass 0.01 kg occupies a volume of 0.003 m 3 at a pressure of 700 KPa and a
temperature of 131ºC. The gas is allowed to expand until the pressure is 100 KPa and the final volume is 0.02
m 3. Calculate:
a) the molecular weight of the gas
b) the final temperature
93. A cubical tank 1 m on a side, contains a mixture of 1.8 kg of nitrogen (M = 28; k = 1.399) and 2.8 kg of an
unknown gas. The mixture pressure and temperature are 290 KPa and 340 K. Determine
a) Molecular weight and gas constant of the unknown gas
b) the volumetric analysis
94. A volume of gas having initial entropy of 5317.2 KJ/K is heated at constant temperature of 540C until the
entropy is 8165.7 KJ/K. How much heat is added and how much work is done during the process.
95. A 283 L drum contains a gaseous mixture at 690 KPa and 38C whose volumetric composition is 30% O2 and
70% CH4. How many kg of mixture must be bled and what mass of O2 added in order to produce at the original
pressure and temperature a mixture whose new volumetric composition is 70% O 2 and 30% CH4.
For O2: M = 32 ; k = 1.395For CH4; M = 16 ; k = 1.321
100. A certain perfect gas of mass 0.01 kg occupies a volume of 0.003 m 3 at a pressure of 700 KPa and a
temperature of 131ºC. The gas is allowed to expand until the pressure is 100 KPa and the final volume is 0.02
m 3. Calculate:
a) the molecular weight of the gas
b) the final temperature
101. When a certain perfect gas is heated at constant pressure from 15ºC to 95ºC, the heat required is 1136 KJ/kg.
When the same gas is heated at constant volume between the same temperatures the heat required is 808
KJ/kg.
Calculate Cp, Cv, k, and M of the gas.
102. A closed vessel of 0.7 m3 internal volume contains a gas at 58 Kpa and 18C and with R = 0.27 KJ/kg-K.If now
0
0.35 kg of another gas at 18C and R = 0.29 KJ/kg-K is also admitted into the vessel. Calculate the final
pressure
of the mixture.
103. A closed system consisting of 2 kg of a gas undergoes a process during which the relationship between
pressure and specific volume is PV1.3 = C. The process begins with P1 = 1 bar, 1 = 0.5 m3/kg and ends with P2
=
0.25 bar. Determine the final volume, in m3, and plot the process on a graph of pressure versus specific volum e.
104. Four kilograms of a certain gas is contained within a piston–cylinder assembly. The gas undergoes a process
for
which the pressure - volume relationship is PV 1.5 = C. The initial pressure is 3 bar, the initial volume is 0.1 m 3,
and
the final volume is 0.2 m3. The change in specific internal energy of the gas in the process is U = - 4.6 kJ/kg.
There are no significant changes in kinetic or potential energy. Determine the net heat transfer for the process,
in
kJ. (Q = -0.8 KJ)
105. Calculate the change of entropy per kg of air (R = 0.287 KJ/kg-K; k = 1.4) when heated from 300K to 600K
while
the pressure drops from 400 KPa to 300 KPa. (S = 0.78 KJ/kg-K)
106. A 5 kg quantity of oxygen (M = 32; k = 1.395) is heated from 250 K to 400 K at constant pressure. Determine
a. h
b. U
c. S
d. W = P dV
107. A 5 m3 tank contains chlorine (R = 0.1172 KJ/kg-K) at 300 KPa and 300K after 3 kg of chlorine has been used.
Determine the original mass and pressure if the original temperature was 315 K. (45.66 kg ; 337.15 KPa)
108. A gaseous mixture has the following volumetric analysis: O2 = 30%; CO2 = 40% ; N2 = 30%. Determine the
gravimetric analysis the partial pressure of each component if the total pressure is 100 KPa and the
temperature is 32C the molecular weight and gas constant of the mixture
For
O2: M = 32 ; k = 1.395
CO2: M = 44 ; k = 1.288
N2: M = 28 ; k = 1.399
109. How many kilograms of N2 must be mixed with 3.6 kg of CO2 in order to produce a gaseous mixture that is 50%
by volume of ach constituents.
110. For the resulting mixture, determine M and R, and the partial pressure of the N2 if that of the CO2 is 138 KPa.
111. The exhaust from a diesel engine using a high grade hydrocarbon fuel has an Orsat Analysis of, 10.2% CO 2 ;
7.9% O2 and 81.9% N2.Determine
a. the value of n and m from CnHm
b. the ratio of H to C in the fuel by mass
c. the actual air fuel ratio
d. the theoretical air – fuel ratio
d the percent excess air
Given:
Orsat Analysis
CO2 = 10.2 %
O2 = 7.9 %
N2 = 81.9 %
Volumetric analysis
CO2 = 8%
H2O = 15.08%
O2 =3.88%
N2 = 73.04%
M = 27.93 kg/kgm
R = 0.298 KJ/kg-K
Orsat analysis
CO2 = 9.42%
O2 = 4.57%
N2 = 86%
113. A gas fired thermal power plant uses two types of hydrocarbon fuel with the following molal (volumetric analysis)
CH4 = 68% ; C2H6 = 32%. Fuel and air is supplied to the boiler at 101 KPa and 25C with 30% excess air
requirement for complete combustion. Product temperature and pressure are 1000C and 101 KPa,
respectively.
Determine the following:
a. the combustion equation
b. the theoretical and actual air fuel ratio
c. the Orsat analysis of the products
d. the molecular weight and gas constant of the products
e. the kg of CO2 formed per kg of fuel burned
f. the partial pressure of H2O in the products
Orsat Analysis
CO2 = 9.3%
O2 = 5.24%
N2 = 85.45%
Molecular Weight and Gas Constant
M = 28.05
R = 0.296
Kg of CO2/kg of fuel =58.08/20.48 = 2.84 kg/kg
PH2O = 14.24 KPa
114. Air is contained in a cylinder fitted with a frictionless piston. Initially the cylinder contains 500 L of air at 150 KP a
and 20 C. The air is then compressed in a polytropic process ( PV n = C) until the final pressure is 600 KPa, at
which point the temperature is 120 C. Determine the work W and the heat transfer Q. (R = 0.287 KJ/kg-K ; k =
1.4)
Given:
V1 = 0.50 m3 ; P1 = 150 KPa ; T1 = 293 K
P2 = 600 KPa ; T2 = 393 K ;
Process: PVn = C
T P n1
n
P1V1
m RT 0.892kg
T1 P1
2 2
1
T U mCv (T2 - T1 ) 64
ln 2
KJ R
n1 T1 Cv k - 1
n ln P2
P1 Q 31 KJ
n 1.27
Q U W
P V T
W 1 1 2 1 95 KJ
1 n T1
115. A steam turbine of a coal fired thermal power plant receives steam at 7 MPa and 500C (h1 = 3410.3 KJ/kg ; S1 =
6.7975 KJ/kg-K) with a velocity of 30 m/sec and expands isentropically to the condenser at a pressure of 20 KPa
with a velocity of 90 m/sec. Calculate the ideal power developed by the turbine for a steam flow rate of 37.8 kg/sec
assuming PE in the turbine to be negligible.
At 20 KPa
Sf = 0.8320 KJ/kg-K ; Sg = 7.9085 KJ/kg-K ; Sfg = 7.0765 KJ/kg-K
hf = 251.4 KJ/kg ; hg = 2609.7 KJ/kg ; hfg = 2358.3 KJ/kg
SOLUTION:
6.7975 = O.8320 + x2(7.0765)
x2 = 0.839
h2 = 251.4 + (0.839)(2358.3) = 2230.014 KJ/kg
Q h KE PE W
Q 0 and PE 0
W -h- KE
116. Air which is initially at 120 KPa and 320K occupies 0.11 m3. It is compressed isothermally until the volume is
halved and then compressed it at constant pressure until the volume decreases to ¼ of the initial volume. Sketch
the process on the PV and TS diagrams. Then determine the pressure, the volume and temperature in each state.
(For air: R = 0.287 KJ/kg-K ; k = 1.4)
Given:
P1 = 120 KPa ; T1 = 320K; V1 = 0.11 m3; T2 = 320K; V2 = ½V1; V3 = ¼V1
For air: R = 0.287 KJ/kg-K; k = 1.4
Processes:
1 to 2: T = C
2 to 3: P = C
P T
3 2
2 1
T=C P=C
1
3
V S
Solution:
At 1 to 2: T = C
P1V1 = P2V2
T1 = T2 = 320K
V2 = ½V1 = ½(0.11) = 0.055 m3
V
P2 P 1 1 120(2) 240 KPa
V2
At 2 to 3: P = C
P3 = P2 = 240 KPa
V3 = ¼V1 = ¼(0.11) = 0.0275 m3
T3 V3
T2
0.0275
160 K
V2
T
3 320
0.055
From
RT
P
1 RT1
P1
2 RT2
P 2
3 RT3
P3
1 = 0.765 m3/kg
2 = 0.383 m3/kg
3 = 0.191 m3/kg
117. A cylinder fitted with a frictionless piston contains 5 kg of superheated water vapor at 1,000 KPa & 250 C (h1 =
2942.6 KJ/kg ; U1 = 2709.9 KJ/kg ; S1 = 6.9247 KJ/kg-K). This system is now cooled at constant pressure until
the water reaches a quality x 2 of 50%. Calculate the heat transferred and the work done during this process, and
draw the process on the PV & TS plane.
At 1000 KPa at saturation
hf = 762.81 KJ/kg; hg = 2778.1 KJ/kg; h fg = 2015.29 KJ/kg
Uf = 761.68 KJ/kg; Ug = 2583.6 KJ/kg ; U fg = 1281.92 KJ/kg
Sf = 2.1387 KJ/kg-K; Sg = 6.5865 KJ/kg-K; Sfg = 4.4478 KJ/kg-K
h2 762.81 (0.50)(2015.26) 1770.44 KJ/kg
U2 761.68 0.50(1281.92) 1402.64KJ/kg
At P C
Q m(h2 - h1 ) 5(1770.44- 2942.6) 5860.8 KJ
U m(U2 - U1 ) 5(1402.64- 2709.9) 6536.3 KJ
W Q - U -5860.8 6536.3 675.5 KJ
P T
1
2 1 2
V S
118. A small circular hole 6 mm in diameter is bored in the side of a large water tank 14 m below the water level in the
tank. The top of the tank is open to the atmosphere and the velocity on the water surface is negligible. Find the
velocity of water exiting the hole and the volume discharged in L/sec. (water = 1000 kg/m3)
1
P 0
W0 2
Q0
KE PE
2 2
v2 v1 g(Z2 Z1 )
2000 1000
v2 2g(Z Z ) v 2
1 2 1
v1 0 ; Z 1 0
v 2 2(9.81)(14) 16.57 m/sec
119. A piston cylinder device, whose piston is resting on a set stops, initially contains 3 kg of air at 200 KPa and 27 C.
The mass of the piston is such that a pressure of 400 KPa is required to move it. Heat is now transferred to the air
until its volume doubles. Determine the work done by the air and the total heat transferred to the air during this
process. Also, show the process on a P-V diagram. (For air: R = 0.287 KJ/kg-K ; k = 1.4)
P T
3
2P = C
2 3
V=
1
1
Q
At V C
V1 V2
P2 T
2
P 1 T1
T2 600 K
Qv 3(0.7175)(600 - 300) 645.75 KJ
At P C
V3 T
3
V 2 T2
3
V3 2V1 2.6 m
2.6 T3
1.3 600
T3 1200 K
Qp mCp (T3 - T2 ) 3(1.0045)(1200- 600)
Qp 1808.1 KJ
W P(V3 - V2 ) 400(2.6-
1.3) W 520 KJ
QT 645.75 1808.1 2453.85 KJ
120.
121. A closed system consisting of 2 kg of a gas undergoes a process during which the relationship between
pressure and specific volume is PV1.3 = constant. The process begins with P1 = 1 bar, 1 = 0.5 m3/kg and ends
with P2 = 0.25 bar. Determine the final volume, in m3, and plot the process on a graph of pressure versus
specific volume. (Note: 100 KPa = 1 Bar)
m = 2 kg
P1 = 1 Bar = 100 KPa ; P2 = 0.25 Bar = 25 KPa
1 = 0.5 m3/kg
Process: PV1.3 = C
P 1 P 2 2
1.3 1.3
1
P1 1.3
1
2
1 2
100 1.3
1
m3
0.5 1.45
2
25 kg
V2 m2 2(1.45) 2.9 m3
122. Suppose that 42,200 KJ of heat energy are supplied in a small boiler to 25 kg of water at 90C. What part of the
water in kg will be vaporized, if the initial enthalpy of water is 376.78 KJ/kg and latent heat of vaporization (h f g)of
water is 2257 KJ/kg. Neglect changes in kinetic and potential energies.
Q m(h2 h1)
42,200
h 376.78 2064.78 KJ/kg
2
25
h2 100(4.187) x2 (2257)
x2 0.793
m
x v
2
m
mv 18.23 kg
mass of water vaporized to vapor
123. Calculate the heat required to be given to 2 kg of ice at -15C to change into steam at atmospheric pressure,
taking the values
Freezing point temperature = 0C
Specific heat of ice = 2.04 KJ/kg-K
Latent heat of fusion = 335 KJ/kg
Specific heat of water = 4.2 KJ/kg-K
Latent heat of evaporation = 2256.7 KJ/kg
Q m2.04(0 15) 335 4.2(100 0) 2256.7
Q 6084.6 KJ
124. A liquid of density 800 kg/m3 specific heat of 2.5 KJ/kg-K and temperature of 27C is mixed with another liquid of
density 820 kg/m3, specific heat 1.9 KJ/kg-K and temperature of 55C in the ratio of one of the first liquid to three
of the second by volume. Find the resulting temperature.
Qh = Qc
mh(Cph)(55 - t) = mc(Cpc)(t – 27)
Vc 1
; V 3V
h c
Vh 3
m
V
m
V
m V
mc Vcc
mh Vhh
3Vc (820)(1.9)(55 t) Vc (800)(2.5)(t 27)
(55 t) 0.428(t 27)
55 t 0.428t 11.55
55 11.55
t 46.6C
1.428)
A 3 m diameter by 4.5 m height vertical tank is receiving water ( = 978 kg/m3) at the rate of 1.13 m 3/min and is
discharging through a 150 mm with a constant velocity of 1.5 m/sec. At a given instant, the tank is half full.
Find the water level and the mass change in the tank 15 minutes later.
Two gaseous streams containing the same fluid enter a mixing chamber and leave as a single stream. For the first
gas the entrance condition are: A1 = 500 cm2 ; v1 = 730 m/sec ; 1 = 1.60 kg/m3. For the second gas the
entrance condition are A2 = 400 cm2; m2 = 8.84 kg/sec ; 2 = .502 m3/kg. The exit stream conditions is: v3 = 130
m/sec and 3 = 0.437 m3/kg.
Determine
(a) the total mass flow leaving the chamber
(b) the velocity of gas 2.
In determining the specific heat of a new metal alloy,0.15 kg of the substance is heated to 400 C and then placed
in a 0.2 kg aluminum calorimeter cup containing 0.4 kg of water at 10C. If the final temperature of the mixture
is 30.5C , what is the specific heat of the alloy. (ignore the calorimeter stirrer and thermometer)
Cpal = 0.92 KJ/kg-C; Cpw = 4.187 KJ\kg-C
It is required to lift five people on an elevator a distance of 100 m. The work is found to be 341.2 KJ and g = 9.75
m/sec2. Determine the average mass per person.
Twenty kilograms of ice at -8C is placed in a 120 kgs of water at 40C. Assuming no heat lost to or absorbed from
the surroundings, what will be the resulting equilibrium temperature of the mixture.
Specific heat of ice = 2.22 KJ/kg-C
Specific heat of water = 4.19 KJ/kg-C
Freezing point temperature of water = 0C
hF of ice = 334.9 KJ/kg
A cup of coffee of volume 0.3 L is heated from a temperature of 25oC to 60oC at a pressure of 100 kPa. Determine the
change in the (a) internal energy, (b) enthalpy and (c) entropy. Assume the density and specific heat of coffee to be
1100 kg/m3 and 4.1 kJ/kg.K respectively. Employ the SL model. (d) What-if scenario: How would the answers change
if the heating was done inside a chamber pressurized at 1 MPa? [Manual Solution] [TEST Solution]
Answers: (a) 47.36 kJ (b) 47.36 kJ (c) 0.15 kJ/kg.K (d) No changes
A block of solid with a mass of 10 kg is heated from 25oC to 200oC. If the change in the specific internal energy is
found to be 67.55 kJ/kg, identify the material. [Manual Solution] [TEST Solution]
Answers: Copper
A block of aluminum with a mass of 10 kg is heated from 25oC to 200oC. Determine (a) the total change in internal
energy and (b) entropy of the block. (c) What-if-Scenario: How would the answer in (b) change if the block was made of
copper instead? [Manual Solution] [TEST Solution]
Answers: (a) 1578.5 kJ/kg (b) 4.17 kJ/K (c) 1.783 kJ/K
A 2 kg block of aluminum at 600oC is dropped into a cooling tank. If the final temperature at equilibrium is 25oC,
determine (a) Change in internal energy, and (b) change in entropy of the block as the system. Use the SL model for
aluminum (c_v = 0.902 kJ/kg.K). [Manual Solution*] [TEST Solution*]
Answers: (a) -1037.3 kJ (b) -1.939 kJ/K
10 A copper block of mass 5 kg, initially at equilibrium with the surroundings at 30oC and 100 kPa is placed in a
pressurized chamber with a pressure of 20 MPa and a temperature of 200oC. Determine (a) the change in the internal
energy (b) enthalpy and (c) entropy of the block after it comes to a new equilibrium. (d) What-if-Scenario: How would
the answer in (a) change if the block was made of silver? [Manual Solution] [TEST Solution]
Answers: (a) 65.62 kJ/kg (b) 67.85 kJ/kg (c) 0.17 kJ/kg.K (d) 39.94 kJ/kg
A 2 kg block of aluminum at 60oC is dropped into a tank containing 5 kg of water at 25oC. If the final temperature after
equilibrium is 27.77oC. Determine (a) DU and (b) DS for the combined system of aluminum and water before and after
the process. [Manual Solution] [TEST Solution]
Answers: (a) -52.35 kJ (b) -0.1643 kJ/K
] A cup of coffee cools down by transferring heat to the surroundings at a rate of 0.1 kW. If the mass of coffee is 0.2 kg
and coffee can be modeled as water, determine the rate of change of temperature of coffee. [Manual Solution][TEST
Solution]
Answers: (a) 1.2 K/s Anim. 3-2-14 (click)
A pump raises the pressure of liquid water from 50 kPa to 5000 kPa in an isentropic manner. Determine (a) the change
in temperature and (b) specific enthalpy between the inlet and exit. [Manual Solution] [TEST Solution]
Answers: (a) 0 (b) 4.965 kJ/kg
Oil (cv=1.8 kJ/kg.K) flows steadily through a long insulated constant-diameter pipe at a volume flow rate of 10 m3/min.
The conditions at the inlet are p = 3000 kPa, T = 20oC, V=20 m/s and z=100 m. The conditions at the exit are p = 2000
kPa, T = 21oC and z=0 m. (a) Use the mass equation to evaluate the velocity at the exit. (b) Use the energy equation
to show that j remains unchanged between the inlet and the exit. (c) Determine the exit temperature. [Manual Solution]
[TEST Solution]
Answers: (a) 20 m/s (b) 21.16oC
Water flows steadily through a device at a flow rate of 20 kg/s. At the inlet the conditions are 200 kPa and 10oC. At the
exit the conditions are 2000 kPa and 50oC. (a) Determine the difference between the entropy transported by the flow at
the exit and at the inlet. (b) What are the possible reasons behind the increase in entropy transport? [Manual Solution]
[TEST Solution]
Answers: (a) 11.06 kW/K (b) heat addition and irreversibilities
19 In an isentropic nozzle, operating at steady state, the specific flow energy 'j' and specific entropy 's' remain constant
along the flow. The following properties are known at the inlet and exit ports of an isentropic nozzle discharging water
at a steady rate of 2 kg/s. Inlet: p=300 kPa, A=4 cm2; Exit: p=100 kPa. Determine (a) the exit velocity and (b) the exit
area. Use the SL model for liquid water. (c) What-if scenario: How would the exit velocity change if the inlet kinetic
energy was neglected? [Manual Solution] [TEST Solution]
Answers: (a) 20.65 m/s (b) 97.2 mm2 (c) 20.03 m/s Anim. 3-2-19 (click)
A pipe carries saturated liquid water at a pressure of 500 kPa. Some water squirts out from the pipe through a small
leak. As the water is expelled, it quickly achieves mechanical equilibrium wit h the atmosphere at 100 kPa. (a) Estimate
the temperature of water inside and outside the pipe. What if scenario: How would the answers change if the fluid was
(b) R-134a or (c) R-12 instead? [Manual Solution] [TEST Solution]
Answers: (a) 151.8oC, 99.6oC (b) 15.6oC, -26.6oC (c) 15.6oC, -30.1oC
A vertical piston-cylinder assembly contains water. The piston has a mass of 2 kg and a diameter of 10 cm. Determine
the vertical force necessary on the piston to ensure that water inside the cylinder boils at (a) 120oC or (b) 80oC.
Assume atmospheric pressure to be 101 kPa. (c) What-if scenario: How would the answer in part (a) change if the
piston mass was neglected? [Manual Solution] [TEST Solution]
Answers: (a) 0.746 kN (b) -0.441 kN (c) 0.766 kN Anim. 3-3-8 (click)
A vertical piston-cylinder assembly contains a saturated mixture of water at 120oC and a gage pressure of 108.5 kPa.
The piston has a mass of 5 kg and a diameter of 12 cm. Determine (a) the atmospheric pressure outside and (b) the
external force exerted on the piston to maintain a constant pressure. [Manual Solution]
Answers: (a) 90 kPa (b) 1.178 kN downward
A cooking pan with an inner diameter of 20 cm is filled with water and covered with a lid of mass 5 kg. If the
atmospheric pressure is 100 kPa. Determine (a) the boiling temperature of water. (b) What-if-Scenario: How would the
answer change if a 5 kg block is placed on top of the lid? [Manual Solution] [TEST Solution]
Answers: (a) 100.04 oC (b) 100.45 oC. Anim. 3-3-10 (click)
11 A heat engine cycle is executed with ammonia in the saturation dome. The pressure of ammonia is 1.5 MPa during
heat addition and 0.6 MPa during heat rejection. What is the highest possible thermal efficiency? Based on the
temperatures of heat addition and rejection, could you comment on possible application of such a low-efficiency cycle?
[Manual Solution] [TEST Solution]
Answers: 9.44% Anim. 3-3-11 (click)
16 A 10 L rigid tank contains 0.01 kg of steam. Determine the (a) pressure (b) stored energy E and (c) entropy S of
steam if the quality is 50%. Neglect kinetic and potential energy. (d) What-if scenario: How would the answers change
if the quality was 100%? [Manual Solution] [TEST Solution]
Answers: (a) 83.7 kPa (b) 14.48 kJ (c) 0.043 kJ/K (d) 175.4 kPa, 25.25 kJ, 0.072 kJ/K Anim. 3 -3-16 (click)
A tank contains 20 kg of water at 85oC. If half of it (by mass) is in the liquid phase and the rest in vapor phase, determine
(a) the volumetric quality, and the stored energy in the (b) liquid and (c) vapor phases. [Manual Solution] [TEST
A vessel having a volume of 0.5 m3 contains 2 kg saturated liquid and saturated vapor mixture of H2O at 500 kPa.
Calculate the (a) mass and (b) volume of each phase. [Manual Solution] [TEST Solution]
Answers: (a) 1.32 kg, 0.67 kg, (b) 0.001 m3, 0.25 m3
A rigid tank of volume 83 m3 contains 100 kg of H2O at 100oC. The tank is heated until the temperature inside reaches
120oC. Determine the pressure inside the tank at the (a) beginning and (b) end of the heating process. What -if-
scenario: How would the final pressure change if the tank temperature increased to 125oC? [Manual Solution] [TEST
Solution]
Answers: (a) 101 kPa (b) 198.5 kPa (c) 216.2 kPa
A rigid tank (v = constant) contains 8 kg of liquid and 2 kg of vapor of H2O at 200oC. To what temperature should the
tank be heated until all the liquid in the tank vaporize? [Manual Solution] [TEST Solution]
Answers: 288oC
A piston cylinder device of volume 1 m3 contains 3 kg of water. The piston, which has an area of 100 cm2, exerts a
force of 1.7 kN on the pin that keeps it from moving. Determine the (a) temperature and (b) quality of H2O inside the
cylinder. The water is now heated. (c) Determine the force on the pin when all the liquid in the tank vaporize. Assume
the atmospheric pressure to be 100 kPa and neglect the piston mass. [Manual Solution] [TEST Solution]
Answers: (a) 130 oC (b) 0.497 (c) 4.64 kN Anim. 3-3-29 (click)
30 A rigid tank with a volume of 3.5 m3 contains 5 kg of saturated liquid-vapor mixture of H2O at 80oC. The tank is
slowly heated until all the liquid in the tank are completely vaporized. Determine the temperature at which this happens.
Also show the process on T-v diagram with respect to saturation lines. [Manual Solution] [TEST Solution]
Answers: 128.33 oC
A 50 L rigid tank contains R-134a at a temperature of 50oC with a quality of 2.5%. Heat is added until the all the vapor
condense (due to increased pressure) and the tank is filled completely with saturated liquid. (a) With the aid of a T -v
diagram, show that this is quite possible. Also determine (b) the pressure and (c) temperature in the tank at saturation.
[Manual Solution] [TEST Solution]
32 A 1000 L rigid tank contains saturated liquid water at 40oC. (a) Determine the pressure inside. (b) The tank is now
heated to 90oC. Use the compressed liquid table to determine the pressure in the tank. [Manual Solution] [TEST
Solution] Table B-4: Compressed
Liquid Table of Water
Answers: (a) 1.407 kg (b) 4400.4 kJ (c) 120.7 kPa (d) 105.0oC
38 A large industrial tank of volume 200 m3 is filled with steam at 450oC and 150 kPa. Determine (a) the pressure and
(b) quality of steam when the temperature drops to 25oC due to heat loss. (c) If the heat transfer for this constant volum
e process is given by Q=DU, determine the heat transfer. [Manual Solution] [TEST Solution]
A piston-cylinder device contains 3 kg of saturated mixture of water with a quality of 0.8 at 180oC. Heat is added until
all the liquid vaporize. Determine (a) the pressure (b) the initial volume (c) the final volume and (d) the work performed
by the vapor during the expansion process. (e) Show the process on a p-v diagram. [Manual Solution] [TEST Solution]
Answers: (a) 1 MPa (b) 0.466 m3 (c) 0.582 m3 (d) 116 kJ Anim. 3-3-43 (click)
45 A piston-cylinder device contains 0.6 kg of steam at 350oC and 1.5 MPa. Steam is now cooled at constant pressure
until half of the mass condenses. Determine (a) the final temperature and (b) the boundary work transfer. (c) Show the
process on a T-s diagram. [Manual Solution] [TEST Solution]
Answers: (a) 198.3oC (b) -108 kJ
Water vapor (1 kg) at 0.2 kPa and 30oC is cooled at a constant pressure process until condensation begins. Determine
(a) the boundary work transfer and (b) change of enthalpy, DH, treating water as the system. (c) What-if-Scenario: How
would the answers change, if all the vapor condensed? [Manual Solution] [TEST Solution]
A piston cylinder device contains 10 L of liquid water at 100 kPa and 30oC. Heat is transferred at constant pressure
until the temperature increases to 200oC. Determine the change in the (a) total volume and (b) total internal energy of
steam. Show the process on a T-s and P-v diagram. [Manual Solution] [TEST Solution]
A piston-cylinder device contains a saturated mixture of water with a quality of 84.3% at 10 kPa. If the pressure is
raised in an isentropic (constant entropy) manner to 5000 kPa, (a) determine the final temperature. (b) What-if
scenario: How would the answer change if water was at saturated vapor state to start with? [Manual Solution] [TEST
Solution] Answers: (a) 499oC (b) 994oC Anim. 3-3-48 (click)
Water at a pressure of 50 MPa is heated in a constant pressure electrical heater from 50oC to 1000oC. Spot the states
on a T-s diagram and determine (a) the change of enthalpy and (b) entropy. Use compressed liquid model for liquid
water. [Manual Solution*] [TEST Solution]
Answers: (a) 4241 kJ/kg (b) 6.31 kJ/kg.K, Anim. 3-3-52 (click)
Determine (a) the mass flow rate and (b) the volume flow rate of steam flowing through a pipe of diameter 0.1 m at a
pressure of 1000 kPa and a temperature of 300oC with a velocity of 50 m/s. (c) Also determine the rate of transport of
energy by the steam. (d) What-if-Scenario: How would the answer in (d) change if the temperature was 400oC? [Manual
Solution] [TEST Solution]
Answers: (a) 1.52 kg/s (b) 0.392 m3/s (c) 4647 kW (d) 4182 kW Figure 3-3-53
Refrigerant-134 flows through a pipe of diameter 5 cm with a mass flow rate of 0.13 kg/s at 100 kPa, 10 m/s. Determine
(a) the temperature and (b) quality of the refrigerant in the pipe. Also determine the rate of transport of (c) energy and
(d) entropy by the flow. [Manual Solution] [TEST Solution]
Answers: (a) -26.6oC (b) 78.3% (c) 24.19 kW (d) 0.0983 kW/K
Steam at a pressure of 2 MPa and 400oC flows through a pipe of diameter 10 cm with a velocity of 50 m/s. Determine
the flow rates of (a) mass (b) energy and (c) entropy. [Manual Solution] [TEST Solution]
Answers: (a) 53.92 m/s (b) 125.8 kW (c) 2,676.95 kW (d) 125.79 kW, 2,675.5 kW
Water is pumped in an isentropic (constant entropy) manner from 100 kPa and 25oC to 40 MPa. Determine the change
in enthalpy, Dh, using the (a) compressed liquid table (b) compressed liquid model and (c) solid/liquid model. [Manual
Solution] [TEST Solution]
Answers: (a) 40.94 kJ/kg (b) 39.99 kJ/kg.K (c) 40.02 kJ/kg
In an isentropic nozzle the specific flow energy j and entropy s remain constant along the flow. Superheated steam flows
steadily through an isentropic nozzle for which the following properties are known at the inlet and exit ports. Inlet: p=100
kPa, T=400oC, A=100 cm2, Vel=5 m/s; Exit: p=200 kPa. Determine (a) the exit velocity (b) the exit temperature and (c)
the exit area. [Manual Solution] [TEST Solution]
Answers: (a) 630 m/s (b) 302oC(b) 1.36 cm2 Anim. 3-3-61 (click)
1 Determine (a) the mass of air at 100 kPa, 25oC in a room with dimensions 5m x 5m x 5m. (b) How much air must
leave the room if the pressure drops to 95 kPa at constant temperature? (c) How much air must leave the room if the
temperature increased to 40oC at constant pressure? [Manual Solution] [TEST Solution]
Answers: (a) 146 kg (b) 7.3 kg (c) 7.0 kg Figure 3-4-1
A cylinder of volume 2 m3 contains 1 kg of hydrogen at 20oC. Determine the change in (a) pressure (b) stored energy
and (c) entropy of the gas as the chamber is heated to 200oC. Use the PG model for hydrogen. (d) What -if-Scenario:
How would the answer change if the chamber contained carbon-dioxide instead? [Manual Solution] [TEST Solution]
Answers: (a) 371.2 kPa (b) 1,833 kJ (c) 4.88 kJ/kg.K (d) 17 kPa, 118.3 kJ, 0.315 kJ/K Anim. 3 -4-2 (click)
The gage pressure in an automobile tire is measured as 250 kPa when the outside pressure is 100 kPa and
temperature 25oC. If the volume of the tire is 0.025 m3, (a) determine the amount of air in kg that must be bled in order
to reduce the pressure to the recommended value of 220 kPa gage. Use the PG model for air. (b) What -if-scenario:
How would the answer in change if the IG model was used instead? [Manual Solution] [TEST Solution]
11 A piston-cylinder device contains 0.01 kg of nitrogen at 100 kPa and 300oC. Using (a) the PG model and (b) IG
model, determine the boundary work transfer as nitrogen cools down to 30oC. Show the process on a T-s and a p-v
diagram. [Manual Solution] [TEST Solution]
Oxygen at 100 kPa and 200oC is compressed to half its initial volume. Determine the final state in terms of pressure
and temperature if the compression is carried out in an (a) isobaric (b) isothermal and (c) isentropic manner. Use the
PG model for oxygen. [Manual Solution] [TEST Solution]
Answers: (a) -36.5oC (b) 200 kPa (c) 263 kPa, 348oC Anim. 3-4-12 (click)
Air at 15oC and 100 kPa enters the diffuser of a jet engine steadily with a velocity of 100 m/s. The inlet area is 0.2 m2.
Determine (a) the mass flow rate of the air, (b) What-if-scenario: How would the conclusion change if the entrance
velocity was 150 m/s? [Manual Solution] [TEST Solution]
Answers: (a) 24.2 kg/s (b) 36.3 kg/s
Air flows through a nozzle in an isentropic manner from p = 400 kPa, T = 25oC at the inlet to p = 100 KPa at the exit.
Determine the temperature at the exit, modeling air as a perfect gas. [Manual Solution] [TEST Solution]
A 15 L tank contains 1 kg of R-12 refrigerant at 100oC. It is heated until the temperature of the refrigerant reaches
150oC. Determine the change in the (a) internal energy DU and (b) entropy DS. Use the RG model with Lee Kesler
charts. [Manual Solution*] [TEST Solution]
Answers: (a) 28.02 kJ/kg (b) 0.07 kJ/kg.K
A piston cylinder device contains 10 L of nitrogen at 10 MPa and 200 K. It is heated at a constant pressure to a
temperature of 400 K. Determine (a) DH and (b) DS. Use the RG model with Lee Kesler charts. (c) What -if-scenario:
How would the answers change if the PC model was used? If the PC model is always more accurate, then why should
one use the RG model at all? [Manual Solution] [TEST Solution]
Answers: (a) 490.5 kJ (b) 1.8 kJ/K (c) 495.9 kJ, 1.77 kJ/K Anim. 3-5-13 (click)
Consider an ideal gas at 400 K and 100 kPa. As a result of some disturbance, the conditions of the gas change to 404
K and 98 kPa. Estimate the change in the specific volume of the gas using the ideal-gas relation at each state. [Manual
Solution*]
Determine the enthalpy change and the entropy change of carbon di-oxide per unit mass as it undergoes a change of
state from 250 K and 7 MPa to 280 K and 12 MPa, (a) by assuming ideal-gas behaviour, and (b) by accounting for the
deviation from ideal-gas bahaviour.
Methane is compressed adiabatically by a steady-state flow compressor from 2 MPa and -10oC to 10 MPa and 110oC
at a rate of 0.8 kg/s. Using the generalized charts, determine the required power input to the compressor.
A cylindrical tank contains 4.0 kg of carbon monoxide at -45 oC has an inner diameter of 0.2 m and a length of 1 m.
Using the RG model (L-K charts), determine (a) the pressure exerted by the gas. (b) (c) What-if-scenario: How would
the answer in (a) change if the IG model is used instead? [Manual Solution] [TEST Solution]
Methane is adiabatically compressed by a piston-cylinder device from 1 MPa and 100oC to 4 MPa. Calculate (a) the
work done per unit mass. Assume the adiabatic efficiency to be 90%. Use the real gas model. (b) What -if-scenario:
How would the answer in (a) change if the gas compressed were ethane instead? [Manual Solution*]
Answers: (a) -277 kJ/kg, (b) -149 kJ/kg
_
BP2-91. In a Rankine cycle, saturated liquid water at 1 bar is compressed isentropically to 150 bar. First by reheating in
a boiler and then by superheating at constant pressure of 150 bar, the water substance is brought to 750K. After
adiabatic reversible expansion in a turbine to 1 bar, it is then cooled in a condenser to a saturated liquid. How much
work is generated in the turbine? (Steam properties h, kJ/kg, s, kJ/kg-K: @ 150 bar&750 K, h = 3240.5, s1 = 6.2549; @
1 bar, hf=417.46, hfg=2258, sf=1.3026, sfg=6.0568)
a. 769.9 b. 796.9 c .967.9d.976.9
BP1-91. A reheat steam has 13850 kPa throttle pressure at the turbine inlet and 2800 kPa reheat pressure. The throttle
and reheat temperature of the steam is 540oC, condenser pressure is 3.4 kPa, engine efficiency of high pressure and
low pressure is 75%. Find the cycle thermal efficiency.
a. 34.46% b. 35.56 c. 36.66d. 37.76
BP2-99 In a Rankine cycle, steam enters the turbine at 2.5 MPa and condenser of 50 kPa. What is the thermal
efficiency of the cycle in percent?
(Steam properties h, kJ/kg, s, kJ/kg-K: @ 2.5 MPa; h g = 2803.1 sg = 6.2575; @ 50 kPa, hf = 340.49, hf g= 2305.4, sf=
1.091, sf g= 6.5029, vf =0.001.3 m3/kg)
a. 25.55 b. 28.87 c. 30.12d. 31.79
BP2-95. A supercritical steam Rankine cycle has turbine inlet conditions of 17.5 MPa and 530 oC expands in a turbine
to 7 kPa. The turbine and pump polytropic efficiencies are 0.9 and 0.7, respectively. Pressure losses between pump
and turbine inlet are 1.5 MPa. What should be the pump work in kJ/kg.
a. 27.13 b. 29.87 c. 32.47d. 33.25
Sol. Wp = vf(P4-P3)/n; vf = 1000 m3/kg
BP2-97 Steam enters the superheater of a boiler at a pressure of 25 bar and dryness of 0.98 and leaves at the same
pressure at a temperature of 370oC. Calculate the heat energy supplied per kg of steam supplied in the superheater.
(Steam properties: @ 25 bar &370oC, h = 3171.8 kJ/kg; @ 25 bar, hf = 962.11, hfg = 1841.0 kJ/kg)
a. 405.51 b. 504.15 c. 154.15 d. 245.25.
A BP2-94. A back pressure steam turbine of 100 MW capacity serves as a prime mover in a cogeneration system. The
boiler admits the return water at a temperature of 66oC and produces the steam at 6.5 MPa and 455oC. Steam then
enters a back pressure turbine and expands to the pressure of the process, which is 0.52 MPa. Assuming a boiler
efficiency of 80% and neglecting the effect of pumping and the pressure drops at various location, what is the
incremental heat rate for electric? The following enthalpies have been found: at turbine entrance = 3306.8 kJ/kg, exit =
2700.8 kJ/kg; boiler entrance = 276.23 kJ/kg, exit = 3306.8 kJ/kg)
a. 22,504.23 kJ/kW-hr b. 52,244.32 kJ/kW-hr
c. 12,435.72kJ/kW-hr d. 32,234.82 kJ/kW-hr
BP2-98. In an open feedwater for a steam power plant, saturated steam at 7 bar is mixed with sub-cooled liquid at 7 bar
and 25oC. Just enough steam is supplied to ensure that the mixed steam leaving the heater will be saturated liquid at 7
bar when heater efficiency is 90%. Calculate the mass flow rate of sub cooled liquid if steam flow rate is 0.865 kg/s.
(Steam properties h, kJ/kg, @ 7 bar, h g = 2763.5, hf = 697.22; @ 7 bar & 25oC, hf = 105.5)
a. 2.725 b. 2.286 c. 3.356d. 3.948
BP2-95. A steam plant operates with an initial pressure of 1.7 MPa and 370oC temperature and exhaust to a heating
system at 0.17 MPa. The condensate from the heating system is returned to the boiler at 65.5oC and the heating
system utilizes from its intended purpose 90% of the energy transferred from the steam it receives. The turbine efficiency
is 70%. If the boiler efficiency is 80%, what is the cogeneration efficiency of the system in percent? Neglect pump work.
(Steam properties h, kJ/kg, s, kJ/kg-K: @ 1.7 MPa & 370oC; h = 3787.1, s = 7.1081; @ 1.7 MPa, hf = 483.20, hfg=
2216.0, sf = 1.4752, s f g= 5.7062; @ 65oC, hf =274.14)
a. 69 b. 78 c. 91.24d. 102.10
BP1-96. In a cogeneration plant, steam enters the turbine at 4 MPa and 400oC. One fourth of the steam is extracted
from the turbine at 600kPa pressure for process heating. The remaining steam continues to expand to 10 kPa. The
extracted steam is then condensed and mixed with feedwater at constant pressure and the mixture is pumped to the
boiler pressure of 4 MPa. The mass flow rate of the steam through the boiler is 30 kg/s. Disregarding any pressure
drops and heat losses in the piping, and assuming the turbine and pump to be isentropic, how much process heat is
required in kW? (Steam properties h, kJ/kg, s, kJ/kg-K: @ 4 MPa & 400oC, h = 3213.6 s = 6.7690; @ 600 kPa, hf =
670.56, hf g= 2086.3, s f = 1.9312, sf g= 4.8288)
a. 1,026.90 b. 2,468.2 c. 3,578.5 d. 15,646.8
BP1-96. A 23.5 kg/s at 5 MPa and 400oC is produced by a steam generator. The feedwater enters economizer at 145o C
and leaves at 205oC. The steam leaves the boiler drum with a quality of 98%. The unit consumes 2.75 kg of coal per
second as received having an heating value of 25,102 kJ/kg. What would be the overall efficiency of the unit in percent?
(Steam properties h, kJ/kg, s, kJ/kg-K: @ 5 MPa & 400oC, h=3195.7; @ 0 MPa, h f = 1154.23, hf g= 1640.1; @ 205oC ,
hf = 610.63)
a. 65 b. 78 c. 88 d. 95
BP2-94. A coal-fired power plant has a turbine-generator rated at 1000 MW gross. The plant required about 9% of this
power for its internal operations. It uses 9800 tons of coal per day. The coal has a heating value of 6,388.9 kCal/kg,
and the steam generator efficiency is 86%. What is the net station efficiency of the plant in percent?
a. 30.12 b. 33.07 c. 36.74d. 40.01
BP2-97. Steam enters the turbine of a cogeneration plant at 7 MPa and 500oC. Steam at a flow rate of 7.6 kg/s is
extracted from the turbine at 600 kPa pressure for process heating. The remaining steam continues to expand to 10
kPa. The recovered condensates are pumped back to the boiler. The mass flow rate of steam that enters the turbine is
30 kg/s. Calculate the cogeneration efficiency in percent. (Steam properties h, kJ/kg, s, kJ/kg-K: @ 7 MPa & 500oC, h
= 3410.3 s = 6.7975; @ 600 kPa, hf = 670.56, hf g= 2086.3, sf = 1.9312, sf g= 4.8228; @ 10 kPa, hf = 191.83, hf g= 2392.8,
sf = 0.6493, sf g= 7.5009)
a. 50 b. 55 c. 60 d. 65
BP2-96. A 60 MW turbine generator running at 3600 rpm receives steam at 4.0 MPa and 450oC with back pressure of
10 kPa. Engine efficiency is 78% and the combined mechanical and electrical efficiency is 95%. What would be the
exhaust enthalpy of the steam in kJ/kg.
a. 2,400.12 kJ/kg b. 20,432.10 kJ/kg
c. 28,124.20 kJ/kg d. 30,101.15 kJ/kg
BP2-95. Steam enters a throttling calorimeter at a pressure of 1.03 MPa. The calorimeter downstream pressure and
temperature are respectively 0.100 MPa and 125 oC. What is the percentage moisture of the supply steam? (Steam
properties h, kJ/kg, s, kJ/kg-K: @1.03 MPa, hfg = 2010.7, hg = 2779.25; @ 0.1 MPa & 125oC, h=2726.6)
a. 1.98 b. 2.62 c.3.15 d. 5.21
BP2-97. Steam expands adiabatically in a turbine from 2 MPa, 400oC to 400 kPa, 250oC. What is the effectiveness of
the process in percent assuming an atmospheric temperature of 15 oC. Neglect changes in kinetic and potential energy.
(Steam properties h, kJ/kg, s, kJ/kg-K: @ 2.0 MPa and 400oC; h = 3247.6 s = 7.1271; @ 400 kPa & 250oC, h= 2964.2,
s= 7.3789)
a. 79.62 b. 84.52 c. 82.45d. 74.57
BP2-93. A drum containing steam with 2.5 m in diameter is 7.5 m long. Of the total volume, 1/3 contains saturated
steam at 800 kPa and the other 2/3 contains saturated water. If this tank should explode, how much water would
evaporat e? Consider the process to be of constant enthalpy. (Steam properties h, kJ/kg, v, m3/kg @0.8 MPa, hf =
721.11, hg = 2769.1, vf= 0.0011148, vg=0.2404; @ 0.101325 MPa & 100oC, hf=419.04, hg=2676.1, vf=0.0010435,
vg=2769.1)
a. 2,123.76 kg b. 2,424.62 kg
c. 2,651.24 kg d. 2,948.11 kg
BP2-92. A Batangas base industrial company operates a steam power plant with reheat and regeneration. The steam
enters a turbine at 300 bar and 900 K and expands to 1 bar. Steam leaves the first stage at 30 bar and part of it entering
a closed heater while the rest reheated to 800K. Both section of the turbine have adiabatic efficiency of 93%. A
condensate pump exists between the main condenser and the heater. Another pump lies between the heater and
condensate outlet line from the heater (condensed extracted steam). Compute for the extracted fraction of the total
mass flow to the heater.
a. 0.234 b. 0.543 c. 0.765 d. 0.485
1. A furnace burns natural gas with the volumetric analysis as follows:CH4 = 85% ; C2H6 =12% ; C3H8 =
3% The gas flow rate is o.37 m3/sec and 25% excess air is required for complete combustion. Air and fuel
enters the furnace at 25C and 101.325 KPa. Determine
a. The actual air-fuel ratio
b. The volumetric analysis of the products
c. The orsat analysis
d. The dew point temperature of the products
2. A steam generator burns fuel with 20% excess air. The fuel oil may be represented by C 14H30. The flue
gases leave the preheater at 310 KPa. Find the minimum stack temperature to avoid condensation.
3. A gas turbine power plant receives an unknown type of hydrocarbon fuel. The fuel is burned with air
yielding the following Orsat analysis of the products of combustion.CO 2 = 10.5% ; O2 = 5.3% ;
N2 = 84.2% . Determine the percent excess air.
4. For a fuel oil with this ultimate analysis: C = 83.7% ; H 2 = 12.7% ; O2 =1.2% ; N2 = 1.7% ; S = 0.7% ;
Assume combustion air to have a dry bulb temperature of 27C and a wet bulb temperature of 21C with
30% excess air for complete combustion. Determine the total combustion gas volume per kg fuel at
205C and 101 KPa.
5. A circular oil tank 10 m long and 1.5 m diameter is used for fuel oil storage. Calculate the number of
days oil supply the tank can hold for continuous operation at the following conditions:
Steam flow - 1050 kg/hr
Steam dry and saturated at 1.4 MPa
Feedwater temperature - 110C
Boiler efficiency - 75%
Fuel oil - 34API
6. There are 20 kg of flue gases formed per kg of fuel burned in the combustion of a fuel oil C12H26. What
is the excess air in percent?
7. A fuel has the following volumetric analysis:
CH4 = 68% C2H6 = 32%
Assume complete combustion with 15% excess air at 101.325 KPa, 21C What is the partial pressure of
the water vapor in Kpa and the dew point temperature of the products.
8. A gravimetric analysis of a typical automotive gasoline gives 86% C and 14% H 2. What average chemical
formula in the form of CnHm, approximates this fuel.
9. A gaseous fuel that is derived from coal has the following volumetric analysis: H2, 47.9% ; CH4, 33.9% ;
C2H4,5.2% ; CO, 6.1% ; CO2 2.6% ; N2, 3.7% ; and O2, 0.6% . It is burn with 110% theoretical air.
Determine
the volume flow rate of air required per unit volume of the gas when both are measured at the same P and T.
the dew point temperature of the combustion products, if the total pressure is 2 atmosphere
10. The ultimate analysis of a fuel oil is 85% Carbon and 15% Hydrogen. If this fuel is burned in an internal
combustion engine and requires 15% excess air for complete combustion, determine
a. the combustion equation
b. the actual air fuel ratio
c. the kg of CO2 formed per kg of fuel
d. the Orsat analysis of the products
e. the molecular weight and gas constant of the products
f. the Specific heats Cp and Cv of the products