FACULTY OF ENGINEERING

DEPARTMENT OF MECHANICAL AND MARINE

Thermodynamics (TDN620S)

Assignment 2.0

1. Heat is transferred to a heat engine from a furnace at a rate of 80 MW. If the rate of waste
heat rejection to a nearby river is 50 MW, determine the net power output and the thermal
efficiency for this heat engine.

2. A car engine with a power output of 65 hp (horsepower) has a thermal efficiency of 24 percent.
Determine the fuel consumption rate of this car if the fuel has a heating value of 44, 196 kJ/kg.

3. The food compartment of a refrigerator is maintained at 5 °C by removing heat from it at a

4. The resistance of a platinum wire is fount to be 11,000 ohms at ice point (0 °C), 15.247 ohms
at the steam point (100 °C), and 28.887 ohms at Sulphur point (444.6°C). Find the constants
A and B in the equation and the resistance of the wire at 660 °C.

𝑅 = 𝑅0 (1 + 𝐴𝑡 + 𝐵𝑡 2 )

5. A Carnot refrigerant cycle absorbs heat at 270 K and reject it at 300 K. Calculate.
a) The coefficient of this refrigeration cycle,
b) If the cycle is absorbing 1330 kJ/minute, how many kJ of input work is required per
second to do this refrigeration,
c) If a Carnot heat pump operates between the same temperatures as the above
refrigeration cycle, what is it coefficient of performance.
d) How many kJ/min will the heat pump deliver at 300 K if it absorbs 1130 kJ/min at
270 K
𝑇𝐿
Note: COP of Refrigeration in terms of temperature = 𝑇 −𝑇
𝐻 𝐿

𝑇𝐻
COP of Heat Pump in terms of temperature = 𝑇
𝐻 −𝑇𝐿
 𝑇𝐻 −𝑇𝐿
Efficiency of Heat Engine in terms of temperature = 𝑇𝐻

6. Prove that the thermal efficiency of a Carnot cycle operating between two temperature limits
TH and TL is surely a function of these two temperatures and can be express as.
TL
ƞth = 1 −
TH
7. The Carnot cycle is composed of four totally reversible processes: isothermal heat addition,
isentropic expansion, isothermal heat rejection, and isentropic compression. Draw a block
diagram showing the Carnot engine and reverse Carnot cycle for a refrigerator. Also show the
p-v diagrams of each of these two cycles.

8. A reversible heat engine operates between two reservoirs at temperatures 600 °C and 40 °C.
The engine drives a reversible refrigerator which operates between reservoirs of 40 °C and
-20 °C. The heat transfer to the heat engine is 2000 kJ and the network output of the combined
engine refrigerator plant is 360 kJ.
a) Evaluate the heat transfer to the refrigerant and the net heat transfer to the reservoir
at 40 °C,
b) Reconsider (a) given that the efficiency of the heat engine and the COP of the
refrigerator are 40% for their maximum possible values.

9. A heat engine is used to drive a heat pump. The heat transfer from a heat engine and from the
heat pump are used to heat the water circulating through the radiators of a building. The
efficiency of the heat engine is 27% and the COP of the heat pump is 4. Find the ratio of the
heat transfer to the circulating water to the heat transfer to the heat engine.

10. By means of example explain how internal and external irreversible may be used to evaluate
the difference between energy quality vs quantity.

11. A cold storage is plant is required to store 20 tonnes of fish. The fish is supplied at temperature
of 30 °C. The specific heats of fish are 2.39 kJ/kg. K and 1.26 kJ/kg. K above and below
freezing point respectively. The fish is stored in a cold storage which is maintained at -8 °C.
The freezing point of fish is -4 °C. The latent heat of fish is 235 kJ/kg. The plant requires 75
kW to drive it. Find the refrigeration capacity of the plant and time taken to achieve cooling if
the actual COP of the plant is 0.3 of its Carnot COP.

12. Air at temperature of 15 °C passes through a heat exchanger at velocity of 30/s where the
temperature is raised to 800 °C. The air then enters a turbine with the same velocity of 30/s
and expands until the temperature falls to 650 °C. On leaving the turbine, the air is taken to a
velocity of 60 m/s to a nozzle where it expands until the temperature has fallen to 500 °C. if
the air flow rate is 2 kg/s calculate (a) the rate of heat transfer to the air in the heat exchanger
, (b) the power output from the turbine with no head losses , (c) the velocity at the exit of the
nozzle , assuming no head loses as well . Take the enthalpy of air h= cpt, where cp is the
specific heat of air equal to 1.005 kJ/kg. K and t is temperature in Kelvin. Start by drawing a
net sketch of the path taken by the air.
13. A Carnot heat engine receives heat at 750 K and rejects the waste heat to the environment at
300 K. The entire work output of the heat engine is used to drive a Carnot refrigerator that
removes heat from the cooled space at -15°C at a rate of 400 kJ/min and rejects it to the same
environment at 300 K. Determine (a) the rate of heat supplied to the heat engine and (b) the
total rate of heat rejection to the environment.

14. Prove that the COP of a reversible refrigerator operating between two given temperature is
the maximum.

15. A mass of 1.5 kg of air is compressed in a quasi-static process from 0.1 MPa to 0.7 MPa for
which pv = constant. The initial density is 1.16 kg/m3. Find the work done by the piston to
compress the air

16. A milk chilling unit can remove heat from milk at the rate of 41.78 MJ/h. Heat leaks into the
milk from the environment at an average rate of 4.187 MJ/h. Find the time required for
cooling a batch of milk from 45 °C to 5 °C. Take the specific heat of milk as 4.187 kJ/kg. K.

17. How does the Bernoulli’s equation compare to the S.F.E.E?

18. A nozzle is a device for increasing the velocity of a steady state flowing steam. At the inlet to
a certain nozzle, the enthalpy of the fluid passing through is 3000 kJ/kg and the velocity is 60
m/s. At the discharge end, the enthalpy is 2762 kJ/kg. The nozzle is horizontal and there is
negligible heat loss from it a) Find the velocity at the exit of the nozzle (b) if the inlet area is
0.1 m2 and the specific volume at inlet is 0.187 m2/kg, find the exit area of the nozzle.

19. A solar powered heat engine designed to receive heat from a solar collector plate and rejects
heats to the surrounding atmosphere that is at 30 °C. When a concentrating collector is used
the plate operate at a surface temperature of 250 °C while when a flat plate collector is used
the plate has an operating temperature at 90 °C. From experiments, it was found that for the
concerned location the maximum possible solar heat received is about 1880 kJ/m2 h. Find
the change in minimum area required for a change from flat plate to concentrating collector if
in both cases the heat engine need to generate 1 kW of useful shaft power.

20. A gas flow steadily through a rotary compressor. The gas enters the compressor at 30 °C, a
pressure of 100 kPa, an enthalpy of 391.2 kJ/kg. The gas leaves the compressor leaves the
compressor at 245 °C, a pressure of 0.6 MPa and enthalpy of 534.5 kJ/kg. There is no heat
transfer to or from the gas as it flows through the compressor. (a) Evaluate the external work
done per unit mass assuming gas velocities at entry and exit to be negligible (b) Evaluate the
external work done per unit mass of gas when the gas velocity at entry is 80 m/s and that at
exit is 160 m/s

21. Describe the following non-flow process by showing both their p-v and T-s diagrams and
demonstrating mathematically how heat transfer or supplied, enthalpy, entropy, work done
and internal energy change in each process.
 i. Isobaric process
ii. Isothermal process
iii. Isochoric process
iv. Isentropic process