79

HEAT AND THERMODYNAMICS

Fill in the Blank

1. Earth receives 1400 W/m 2 of solar power. If all the solar energy falling on a lens of area 0.2 m 2 is
focussed onto a `block of ice of mass 280 grams, the time taken to melt the ice will be ….minutes.
(Latent heat of fusion of ice = 3.3  105 J/kg). (1997)

2. A ring shaped tube contains two ideal gases with equal masses and M1 M2
molar masses M1 = 32 and M2 = 28. The gases are separates by one
fixed partition and another movable stopper S which can move freely 
without friction inside the ring. The angle  as shown in the figure is 
…..degrees. S
(1997)

3. A gas thermometer is used as a standard thermometer for measurement of temperature. When

the gas container of the thermometer is immersed in water at its triple point 273.16 K, the
pressure in the gas thermometer reads 3.0  104 N/m2. When the gas container of the same
thermometer is immersed in another system, the gas pressure reads 3.5  104 N/m2. The
temperature of this system is therefore …… C. (1997C)

4. Two metal cubes A and B of same size are arranged as

shown in figure. The extreme ends of the combination
are maintained at the indicated temperatures. The
0 0
arrangement is thermally insulated. The coefficients of 100 C A B 0C

thermal conductivity of A and B are 300 W/m C and

t
200 W/m C, respectively. After steady state is reached,
the temperature t of the interface will be……………. (1996)

5. An ideal gas with pressure P, volume V, and temperature T is expanded isothermally to a volume
2V and a final pressure Pi. If the same gas is expanded adiabatically to a volume 2V, the final
pressure is Pa. The ratio of the specific heats for the gas is 1.67. The ratio Pa/Pi is…………
(1994)

6. A container of volume 1 m 3 is divided into two equal parts by a partition. One part has an ideal
gas at 300 K and the other part is vacuum. The whole system is thermally isolated from the
surroundings. When the partition is removed the gas expands to occupy the whole volume. Its
temperature will now be ……… (1993)

7. A substance of mass M Kg requires a power input of P watts to remain in the molten state at its
melting point. When the power source is turned off, the sample completely solidifies in time t
seconds. The latent heat of fusion of the substance is …………….. (1992)

8. A piece of metal floats on mercury. The coefficients of volume expansion of the metal and
mercury are 1 and  2 respectively. If the temperature of both mercury and the metal are
increased by an amount T, the fraction of the volume of the metal submerged in mercury
changes by the factor ………………… (1991)

9. A solid copper sphere (density  and specific heat c) of radius r at an initial temperature 200K is
suspended inside a chamber whose walls are at almost 0 K. The time required to the temperature
of sphere to drop to 100 K is…… (1991)

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10. A point source of heat of power P is placed at the centre of a spherical shell of mean radius R.
The material of the shell has thermal conductivity K. If the temperature difference between the
outer and inner surface of the shell is not to exceed T, the thickness of the shell should not be
less than…………….. (1991)

11. The earth receives radiation at its surface from the sun at the rate of 1400 W/m2. The distance of
11
the centre of the sun from the surface of the earth is 1.5  10 m and the radius of the sun is 7.0
8
 10 m. Treating the sun as a block body, it follows from the above data that its surface
temperature is ……………..K. (1989)

12. 300 grams of water at 25C is added to 100 grams of ice at 0C. The final temperature of the
mixture is …………….. C. (1989)

13. During an experiment, an ideal gas is found to obey an additional law VP2 = constant. The gas is
initially at a temperature T, and volume V. When it expands to a volume 2V, the temperature
becomes……………… (1987)

14. The variation of temperature of a material as heat is given

to it at a constant rate is shown in the figure. The material
is in solid state at the point O. The state of the material at T C
D
the point P is …………….. A P
B

O Heat Added
(1985)

15. One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas. The molar
specific heat of the mixture at constant volume is …………….. (1984)

True/false

1. Two spheres of same material have radii 1 m and 4 m and temperatures 4000 K and 2000 K
respectively. The energy radiated per second by the first sphere is greater than that by the
second. (1988)

2. The root mean square (rms) speed of oxygen molecules (O2) at a certain temperature T (degree
absolute) is V. If the temperature is doubled and oxygen gas dissociates into atomic oxygen, the
rms speed remain unchanged. (1987)

3. At a given temperature, the specific heat capacity of a gas at constant pressure is always greater
than its specific heat capacity at constant volume. (1987)

4. The curves A and B in the figure show P-V graphs for an

isothermal and an adiabatic process for an ideal gas. The
isothermal process is represented by the curve A. P A

V (1985)

5. Water in a closed tube is heated with one arm vertically

placed above a lamp. Water will begin to circulate along the
tube in counter - clockwise direction
A B
(1983)

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6. A barometer made of a very narrow tube is placed at normal
Vacuum
temperature and pressure. The coefficient of volume
expansion of mercury is 0.00018 per C and that of the tube Hg
is negligible. The temperature of mercury in the barometer
is now raised by 1C, but the temperature of the
atmosphere does not change. Then the mercury height in
the tube remains unchanged. (1983)

7. Two different gases at the same temperature have equal rms speed. (1982)

8. The volume V versus temperature T graphs for a certain V

P2
amount of a perfect gas at two pressures P1 and P2 are as
shown in the figure. It follows from the graphs that P1 is P1
greater than P2.

T (1982)

9. The rms speed of the molecules of different ideal gases, maintained at the same temperature are
the same. (1981)

MCQ-Single Correct
1. A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod.
The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the
metal rod changes with time (t) as
T (t) = T0 (1 + t1/4)
where  is a constant with appropriate dimension while T0 is a constant with dimension of
temperature. The heat capacity of the metal is
4P(T(t)  T0 )4 4P(T(t)  T0 )
(A) 4 5
(B)
 T0 4 T02
4P(T(t)  T0 )2 4P(T(t)  T0 )3
(C) (D) (2019)
4 T02 4 T04

2. A water cooler of storage capacity 120 litres can cool water at a Cooler Device
Hot
constant rate of P watts. In a closed circulation system (as
shown schematically in the figure), the water from the cooler is
used to cool an external device that generates constantly 3 kW of
heat (thermal load). The temperature of water fed into the device
cannot exceed 30 0C and the entire stored 120 litres of water is
initially cooled to 10 0C. The entire system is thermally insulated. Cold
The minimum value of P (in watts) for which the device can be
operated for 3 hours is
-1 -1 -3
(Specific heat of water is 4.2 kJ kg K and the density of water is 1000 kg m ) (2016)
(A) 1600 (B) 2067
(C) 2533 (D) 3933
3. A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state
at pressure Pi = 105 Pa and volume Vi = 10-3 m3 changes to a final state at Pf = (1/32)  105 Pa
and Vf = 8  10-3 m3 in an adiabatic quasi-static process, such that P3V5 = constant. Consider
another thermodynamic process that brings the system from the same initial state to the same
final state in two steps: an isobaric expansion at Pi followed by an isochoric (isovolumetric)
process at volume Vf. The amount of heat supplied to the system in the two-step process is
approximately (2016)
(A) 112 J (B) 294 J
(C) 588 J (D) 813 J

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4. The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of
0 0
the wires has a length of 1 m at 10 C. Now the end P is maintained at 10 C, while the end S is
0
heated and maintained at 400 C. The system is thermally insulated from its surroundings. If the
thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal
expansion of PQ is 1.2  10-5 K-1, the change in length of the wire PQ is (2016)
(A) 0.78 mm (B) 0.90 mm
(C) 1.56 mm (D) 2.34 mm
–2
5. Parallel rays of light of intensity I = 912 Wm are incident on a spherical black body kept in
surroundings of temperature 300 K. Take Stefan-Boltzmann constant  = 5.7×10–8 Wm–2 K–4 and
assume that the energy exchange with the surroundings is only through radiation. The final
steady state temperature of the black body is close to (2014)
(A) 330 K (B) 660 K
(C) 990 K (D) 1550 K

6. Two rectangular blocks, having identical dimensions, can Configuration II

Configuration I
be arranged either in configuration I or in configuration II
as shown in the figure. One of the blocks has thermal 2 
conductivity  and the other 2 . The temperature  2  
x
difference between the ends along the x-axis is the same
in both the configurations. It takes 9 s to transport a
certain amount of heat from the hot end to the cold end (2013)
in the configuration I. The time to transport the same amount of heat in the configuration II is
(A) 2.0 s (B) 3.0 s
(C) 4.5 s (D) 6.0 s

7. Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of
their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The
ratio of their densities is (2013)
(A) 1 : 4 (B) 1 : 2
(C) 6 : 9 (D) 8 : 9

8. A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic
 v (helium) 
mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds  rms  is
 v rms (argon ) 
(A) 0.32 (B) 0.45
(C) 2.24 (D) 3.16 (2012)

9. Three very large plates of same area are kept parallel and close to each other. They are
considered as ideal black surfaces and have very high thermal conductivity. The first and third
plates are maintained at temperatures 2T and 3T respectively. The temperature of the middle
(i.e. second) plate under steady state condition is
1/ 4 1/ 4
 65   97 
(A)   T (B)   T
 2   4 
1/ 4
 97 
(C)   T (D) (97)1/4 T (2012)
 2 

10. Two moles of ideal helium gas are in a rubber balloon at 30C. The balloon is fully expandable
and can be assumed to require no energy in its expansion. The temperature of the gas in the
balloon is slowly changed to 35C. The amount of heat required in raising the temperature is
nearly (take R = 8.31 J/mol.K)
(A) 62 J (B) 104 J
(C) 124 J (D) 208 J (2012)

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11. 5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial
temperature to be T1, the work done in the process is
9 3
(A) RT1 (B) RT1
8 2
15 9
(C) RT1 (D) RT1 (2011)
8 2
12. A real gas behaves like an ideal gas if its (2010)
(A) pressure and temperature are both high (B) pressure and temperature are both low
(C) pressure is high and temperature is low (D) pressure is low and temperature is high

13. An ideal gas is expanding such that PT2 = constant. The coefficient of volume expansion of the
gas is (2008)
1 2
(A) (B)
T T
3 4
(C) (D)
T T

14. In a dark room with ambient temperature T0, a black body is kept at a temperature T. Keeping the
temperature of the black body constant (at T), sunrays are allowed to fall on the black body
through a hole in the roof of the dark room. Assuming that there is no change in the ambient
temperature of the room, which of the following statement(s) is/are correct? (2006)
(A) The quantity of radiation absorbed by the black body in unit time will increase.
(B) Since emissivity = absorptivity, hence the quantity of radiation emitted by black body in unit
time will increase.
(C) Black body radiates more energy in unit time in the visible spectrum.
(D) The reflected energy in unit time by the black body remains same.

15. Which of the following process does not occur through convection (2005)
(A) Boiling of water (B) Land breeze and Sea breeze
(C) Circulation of air around furnace (D) Heating of glass bulb through filament

16. Two litre of water at initial temperature of 270C is heated by a heater of power 1 kW. If the lid of
kettle is opened, then heat is lost at the constant rate of 160 J/s. Find the time required to raise
the temperature of water to 770C with the lid open (Specific heat of water 4.2 kJ/kg)
(A) 5 min 40 sec (B) 14 min 20 sec
(C) 8 min 20 sec (D) 16 min 10 sec (2005)

17. One calorie is defined as the heat required to raise the temperature of 1 gm of water by 10C in a
certain interval of temperature and at certain pressure. The temperature interval and pressure is
0 0 0 0
(A) 13.5 C to 14.5 C & 76 mm of Hg (B) 6.5 C to 7.5 C & 76 mm of Hg
0 0
(C) 14.5 C to 15.5 C & 760 mm of Hg (D) 98.5 C to 99.50C & 760 mm of Hg
0
(2005)

18. Temperature of a gas is 20C and pressure is changed from 1.01  105 Pa to 1.165  105 Pa. If
volume is decreased isothermally by 10%. Bulk modulus of gas is
(A) 1.55  105 (B) 0.155  105
(C) 1.4  105 (D) 1.01105 (2005)

19. A spherical body of area A and emissivity 0.6 is kept inside a perfectly black body. Total heat
radiated by the body at temperature T is
(A) 0.4  AT4 (B) 0.8AT4
4
(C) 0.6 AT (D) 1.0AT4 (2005)

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20. The graph shown in the figure represents energy density E
versus  for three sources sun, welding arc, tungsten E
filament. 3
(A) 1 – Tungsten, 2 – Welding arc, 3 – Sun 2
1
(B) 1 – Sun, 2 – Tungsten, 3 – Welding arc.
O 
(C) 1 – Sun, 2 – Welding arc, 3 - Tungsten (2005)
(D) 1 – Welding arc, 2 – Sun, 3 - Tungsten

21. An ideal gas is initially at P1, V1 is expanded to P2, V2 and then P3

compressed adiabatically to the same volume V1 and pressure P3. If
P1
W is the net work done by the gas in complete process which of the
following is true P2
(A) W > 0 ; P3 > P1 (B) W < 0 ; P3 > P1
(C) W > 0 ; P3 < P1 (D) W < 0 ; P3 < P1 V1 V2

(2004)

22. Two identical rods are connected between two containers one of them is at 100C and another is
at 0C. If two identical rods are connected in parallel then the rate of melting of ice is q1 gm/s. If
they are connected in series then rate is q2 gm/s. Then the ratio q2 / q1 is
(A) 2 (B) 4
(C) 1/2 (D) 1/4 (2004)

23. If liquified oxygen at 1 atmospheric pressure is heated from 50 K to 300 K by supplying heat at
constant rate. The graph of temperature vs time will be (2004)

(A) (B)
T T

t
t

(C) T
(D) T

t t

24. Three discs A, B and C having radii 2, 4, and 6 cm respectively are coated with carbon black.
Wavelength for maximum intensity for the three discs are 300, 400 and 500 nm respectively. If
QA, QB and QC are power emitted by A, B and C respectively, then
(A) QA will be maximum (B) QB will be maximum
(C) QC will be maximum (D) QA = QB = QC (2004)

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25. An ideal gas undergoes a cyclic process as shown in the A
given P-T diagram, where AC is adiabatic. The process is P
also represented by
C
B
T (2003)
(A) A (B) A
P P

B C C B
V V
(D) A (D) A

P P
B
C
B C
V V

26. An aluminium rod (length 1; coefficient of linear expansion a ) and a steel rod (length 2;
coefficient of linear expansion  s ) are joined such that the total length becomes (1 + 2). If the
increase in lengths of aluminium and steel rods is found to be same when the system is raised to
a certain temperature, then the ratio 1  1   2 
(A) a  s (B)  s a
(C)  s  a   s  (D) a   a   s  (2003)

27. 2 kg of ice at 20C is mixed with 5 kg of water at 20C. The water content of the final mixture is
(Latent heat of fusion = 80 kcal/kg, specific heat of water = 1 kcal/kg-C, specific heat of ice = 0.5
kcal/kg-C) (2003)
(A) 7 kg (B) 6 kg
(C) 4 kg (D) 3 kg

28. The temperature (T) versus time (t) graphs of two bodies X and Y with
equal surface areas are shown in the figure. If the emissivity and the
absorptivity of X and Y are Ex < Ey and Ax < Ay respectively, then T
y
(A) Ex > Ey & Ax > Ay (B) Ex < Ey & Ax > Ay
(C) Ex > Ey & Ax < Ay (D) Ex < Ey & Ax < Ay x
t=0 t
(2003)

dV dP
29. Which of the following graphs correctly represents the variation of  =  with P for an
V
ideal gas at constant temperature? (2002)
(A) (B)
 

P
P
(C) (D)
 

P P

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30. An ideal black - body at room temperature is thrown into a furnace. It is observed that
(A) initially it is the darkest body and at later times the brightest.
(B) it is the darkest body at all times.
(C) it cannot be distinguished at all times.
(D) initially it is the darkest body and at later times it cannot be distinguished. (2002)

31. An ideal gas is taken through the cycle ABCA, as

2 C B
shown in the figure. If the net heat supplied to the gas in
the cycle is 5J, the work done by the gas in the process 3
V (m )
CA is
(A) 5J (B) 10J 1 A
(C) 15 (D) 20J
2
P (N/m ) 10
(2002)

32. P – V plots for two gases during adiabatic processes are shown in P
the figure. Plots 1 and 2 should correspond respectively to
(A) He and O2 (B) O2 and He 1
2
(C) He and Ar (D) O2 and N2 V (2001)

33. When a block of iron floats in mercury at 0C, a fraction k1 of its volume is submerged, while at
the temperature 60 C, a fraction k2 is seen to be submerged. If the coefficient of volume
expansion of iron is Fe and that of mercury is Hg, then the ratio k1/k2 can be expressed as
1  60 Fe 1  60Fe
(A) (B)
1  60 Hg 1  60 Hg
1  60 Fe 1  60 Hg
(C) (D) (2001)
1  60 Hg 1  60 Fe

34. Three rods made of the same material and having the same cross-section 900C
have been joined as shown in the figure. Each rod is of the same length. The 0C 0

left and right ends are kept at 0C and 90C respectively. The temperature of 900C
the junction of the three rods will be
(A) 45C (B) 60C
(C) 30C (D) 20C (2001)

35. In a given process on an ideal gas, dW = 0 and dQ < 0. Then for the gas
(A) the temperature will decrease (B) the volume will increase
(C) the pressure will remain constant (D) the temperature will increase (2001)

36. Two monatomic ideal gases 1 and 2 of molecular masses m 1 and m2 respectively are enclosed in
6separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to
that in gas 2 is given by
m1 m2
(A) (B)
m2 m1
m1 m2
(C) (D) (2000)
m2 m1

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37. A monatomic ideal gas, initially at temperature T1, is enclosed in a cylinder fitted with a
frictionless piston. The gas is allowed to expand adiabatically to a temperature T2 by releasing the
piston suddenly. If L1 and L2 are the length of the gas column before and after expansion
T
respectively, then 1 is given by
T2
2
L  3 L1
(A)  1  (B)
 L2  L2
2
L L  3
(C) 2 (D)  2  (2000)
L1  L1 

38. A block of ice at –10C is slowly heated and converted to steam at 100C. Which of the following
curves represent the phenomenon qualitatively? (2000)
(A) (B)

Temperature
Temperature

Heat supplied Heat supplied

(C) (D)

Temperature
Temperature

Heat supplied Heat supplied

39. An ideal gas is initially at temperature T and volume V, its volume increased by V due to an
increase in temperature T, pressure remaining constant. The quantity  = V /(VT) varies with
temperature as
(A) (B)
 

T T + T T T + T
Temp. (K) Temp. (K)
(C) (D)
 

T T + T T T + T
Temp. (K) Temp. (K) (2000)

40. Starting with the same initial conditions, an ideal gas expands from volume V1 to V2 in three
different ways. The work done by the gas is W 1 if the process is purely isothermal, W 2 if purely
isobaric and W 3 if purely adiabatic. Then
(A) W 2 > W1 > W 3 (B) W 2 > W3 > W 1
(C) W 1 > W 2 > W 3 (D) W 1 > W3 > W 2 (2000)

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88
T3
41. The plots of intensity versus wavelength for three black bodies at
temperature T1, T2 and T3 respectively are as shown. Their T T1 T2

temperatures are such that

(A) T1 > T2 > T3 (B) T1 > T3 > T2
(C) T2 > T3 > T1 (D) T3 > T2 > T1 

(2000)

42. The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300 K is
(A) (2 / 7) (B) (1/ 7)
(C) 3 /5 (D) 6 /5 (1999)

43. A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting
all vibrational modes, the total internal energy of the system is
(A) 4RT (B) 15 RT
(C) 9 RT (D) 11 RT (1999)

44. Two identical containers A and B with frictionless pistons contain the same ideal gas at the same
temperature and the same volume V. The mass of the gas in A is m A and that in B is m B. The gas
in each cylinder is now allowed to expand isothermally to the same final volume 2V. The changes
in the pressure in A and B are found to be P and 1.5P respectively. Then (1998)
(A) 4mA = 9mB (B) 2mA = 3mB
(C) 3mA = 2mB (D) 9mA = 4mB

45. A black body is at a temperature of 2880 K. The energy of radiation emitted by this object with
wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between
1499 nm and 1500 nm is U3. The Wien constant b = 2.88  106 nm K. Then
(A) U1 = 0 (B) U3 = 0
(C) U1 > U2 (D) U2 > U1 (1998)

46. A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio
of the average rotational kinetic energy per O2 molecule to that per N2 molecule is
(A) 1 : 1
(B) 1 : 2
(C) 2 : 1
(D) depends on the moments of inertia of the two molecules (1998)

47. A given quantity of an ideal gas is at pressure P and absolute temperature T. The isothermal bulk
modulus of the gas is
2
(A) P (B) P
3
3
(C) P (D) 2P (1998)
2

48. The average translational energy and the rms speed of molecules in a sample of oxygen gas at
300K are 6.21  10-21 J and 484 m/s respectively. The corresponding values at 600K are nearly
(assume ideal gas behaviours)
(A) 12.42  10-21 J, 968m/s (B) 8.78  10-21 J, 684 m/s
-21
(C) 6.21  10 J, 968m/s (D) 12.42  10-21 J, 684m/s (1997)

49. The intensity of radiation emitted by the sun has its maximum value at a wavelength of 510 nm
and that emitted by the North Star has the maximum value at 350 nm. If these stars behave like
blackbodies, then the ratio of the surface temperatures of the Sun and the North star is (1997)
(A) 1.46 (B) 0.69
(C) 1.21 (D) 0.83

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50. The average translational kinetic energy of O2 (molar mass 32) molecules at a particular
temperature is 0.048eV. The translational kinetic energy of N2 (molar mass 28) molecules in eV
at the same temperature is (1997)
(A) 0.0015 (B) 0.003
(C) 0.048 (D) 0.768

51. A vessel contains 1 mole of O2 gas (molar mass 32) at a temperature T. The pressure of the gas
is P. An identical vessel containing one mole of gas (molar mass 4) at a temperature 2T has a
pressure of
(A) P/8 (B) P
(C) 2P (D) 8P (1997)

52. A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. If the radius were
halved and the temperature doubled, the power radiated in watt would be
(A) 225 (B) 450
(C) 900 (D) 1800 (1997)

53. The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K the root-mean-
square velocity of the gas molecules is , at 480 K it becomes (1996)
(A) 4  (B) 2
(C) /2 (D) /4

54. From the following statements concerning ideal gas at any given temperature T, select the correct
one(s)
(A) The coefficient of volume expansion at constant pressure is the same for all ideal gases
(B) The average translational kinetic energy per molecule of oxygen gas is 3kT, k being
Boltzmann constant
(C) The mean-free path of molecules increases with increases in the pressure
(D) In a gaseous mixture, the average translational kinetic energy of the molecules of each
component is different (1995)

55. Three rods of identical cross-sectional area and made from the same metal from the sides of an
isosceles triangles ABC, right-angled at B. The point A and B are maintained at temperatures T
and ( 2 )T respectively. In the steady state, the temperature of the point C is TC. Assuming that
only heat conduction takes place, Tc/T is (1995)
1 3
(A) (B)

2 2 1  2 1
1 1
(C) (D)
3  2 1  2 1

56. Two metallic spheres S1 and S2 are made of the same material and have got identical surface finish.
The mass of S1 is thrice that of S2. Both the spheres are heated to the same high temperature and
placed in the same room having lower temperature but are thermally insulated from each other. The
rate of the initial rate of cooling of S1 to that of S2 is (1995)
1 1
(A) (B)
3 3
1
 1 3
(C) 3 (D)  
3

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57. Three closed vessels A, B and C are at the same temperature T and contain gases which obey
the Maxwellian distribution of velocities. Vessel A contains only O2, B only N2 and C a mixture of
equal quantities of O2, and N2. If the average speed of the O2 molecules in vessel A is V1, that of
the N2 molecules in vessel B is V2, the average speed of the O2 molecules in vessel C is
(A)  v1  v 2  / 2 (B) V1
1
(C)  v1v 2  2 (D) 3kT / M (1992)
where M is the mass of an oxygen molecule.

58. When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy
supplied which increases the internal energy of the gas is
(A) 2/5 (B) 3/5
(C) 3/7 (D) 5/7 (1990)

59. Two rods of different materials having coefficients of thermal expansion 1, 2 and Young’s
modulus Y1, Y2 respectively are fixed between two rigid massive walls. The rods are heated such
that they undergo the same increase in temperature. There is no bending of the rods. If 1:2 =
2:3, the thermal stresses developed in the two rods are equal provided Y1:Y2 is equal to (1989)
(A) 2:3 (B) 1:1
(C) 3:2 (D) 4:9

60. A cylinder of radius R made of a material of thermal conductivity K1 is surrounded by a cylindrical

shell of inner radius R and outer radius 2R made of a material of thermal conductivity K2. The two
ends of the combined system are maintained at two different temperatures. There is no loss of
heat across the cylindrical surface and the system is in steady state. The effective thermal
conductivity of the system is
(A) K1 + K2 (B) K1K2/(K1+K2)
(C) (K1 + 3K2)/4 (D) (3K1 + K2)/4 (1988)

61. If one mole of a monoatomic gas ( = 5/3) is mixed with one mole of a diatomic gas
( = 7/5), the value of  for the mixture is
(A) 1.40 (B) 1.50
(C) 1.53 (D) 3.07 (1988)

62. Steam at 100C is passed into 1.1 kg of water contained in a calorimeter of water equivalent 0.02
kg at 15C till the temperature of the calorimeter and its contents rises to 80C. The mass of the
steam condensed in kg is
(A) 0.130 (B) 0.065
(C) 0.260 (D) 0.135 (1986)

63. 70 Calories of heat is required to raise the temperature of 2 moles of an ideal gas at constant
pressure from 30C to 35C. The amount of heat required (in Calories) to raise the temperature of
the same gas through the same range (30C to 35C) at constant volume is:
(A) 30 (B) 50
(C) 70 (D) 90 (1985)

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64. At room temperature, the rms speed of the molecules of a certain diatomic gas is found to be
1930 m/s. The gas is
(A) H2 (B) F2
(C) O2 (D) Cl2 (1984)

65. An ideal monoatomic gas is taken round the cycle ABCDA P

as shown in the P-V diagram. The work done during the 2P, V 2P, 2V
cycle is B C
(A) PV (B) 2PV
1 A D
(C) PV (D) zero P, V P, 2V
2
V (1983)

66. A wall has two layers A and B, each made of different material. Both the layers have the same
thickness. The thermal conductivity of the material of A is twice that of B. Under thermal
equilibrium, the temperature difference across the wall is 36C. The temperature difference
across the layer A is (1980)
(A) 6C (B) 12C
(C) 18C (D) 24C

67. A constant volume gas thermometer works on (1980)

(A) the principle of Archimedes (B) Boyle’s law
(C) Pascal’s law (D) Charle’s law

68. A metal ball immersed in alcohal weighs W 1 at 0C and W 2 at 50C. The coefficient of cubical
expansion of the metal is less than that of the alcohal. Assuming that the density of the metal is
large compared to that of alcohal, it can be shown that (1980)
(A) W 1 > W 2 (B) W 1 = W 2
(C) W 1 < W 2 (D) can’t determine

Assertion-Reasoning

1. STATEMENT-1
The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5
times the product of its pressure and its volume.
because
STATEMENT-2
The molecules of a gas collide with each other and the velocities of the molecules change due to
the collision.
(A) Statement -1 is True, Statement-2 is True; Statement -2 is a correct explanation for
Statement-1.
(B) Statement -1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for
Statement-1.
(C) Statement -1 is True, Statement-2 is False.
(D) Statement -1 is False, Statement-2 is True. (2007)

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Comprehension-I
Answer the following by appropriately matching the list based on the information given in
the paragraph.

In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the
gas is given by TX, where T is temperature of the system and X is the infinitesimal change in a
thermodynamic quantity X of the system. For a mole of monatomic ideal gas
3  T   V 
X  Rln    Rln   . Here, R is gas constant, V is volume of gas. TA and VA are constants.
2 T
 A  VA 
The List –I below gives some quantities involved in a process and List –II gives some possible
values of these quantities.
List-I List-II
1
(I) Work done by the system in process 1  2  3 (P) RT0 ln2
3
1
(II) Change in internal energy in process 1  2  3 (Q) RT0
3
Heat absorbed by the system in process 1  2
(III) (R) RT0
3
4
(IV) Heat absorbed by the system in process 1  2 (S) RT0
3
50
19 50  1.2 60
Molarity     2.985
(T) 20.1 20.1 20.1
19  1.2

5
(U) RT0
6

1. If the process carried out on one mole of P

monatomic ideal gas is as shown in figure in
1 3P0
the PV-diagram with P0V0 = RT0 , the 3
3 2
correct match is,
1
P0 2

V0 2V0 V
Options
(A) I  Q, II  R, III  S, IV  U
(B) I  Q, II  S, III  R, IV  U
(C) I  Q, II  R, III  P, IV  U
(D) I  S, II  R, III  Q, IV  T (2019)

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2. If the process on one mole of monatomic ideal T
gas is as shown in the TV-diagram with P0V0 = T0 3
1
RT0 , the correct match is,
3 1
T0 2
3

V0 2V0
Options
(A) I  P, II  T, III  Q, IV  T
(B) I  S, II  T, III  Q, IV  U
(C) I  P, II  R, III  T, IV  S
(D) I  P, II  R, III  T, IV  P (2019)

Comprehension-II
Answer Q.1, Q.2 and Q.3 by appropriately matching the information given in the three
columns of the following table.
An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the
corresponding P – V diagrams in column 3 of the table. Consider only the path from state 1 to
2. W denotes the corresponding work done on the system. The equations and plots in the table
have standard notations as used in thermodynamic processes. Here  is the ratio of heat
capacities at constant pressure and constant volume. The number of moles in the gas is n.
Column I Column 2 Column 3
(P)
(I) P 1 2

1 (i)
W12  P2 V2  P1V2  Isothermal
 1
V
(Q)
P
1
(II) (ii)
W12  PV2  PV1 isochoric
2
V
(R)
P 1
2
(III) (iii)
W12  0 Isobaric

V
(S)
P 1
(IV)
V2 (iv)
W1 2  nRT ln( ) Adiabatic
V1
2
V

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3. Which of the following options is the only correct representation of a process in which (2017)
 U   Q  PV ?
[A] (II) (iv) (R) [B] (II) (iii) (P)
[C] (II) (iii) (S) [D] (III) (iii) (P)

4. Which one of the following options is the correct combination? (2017)

[A] (III) (ii) (S) [B] (II) (iv) (R)
[C] (II) (iv) (P) [D] (IV) (ii) (S)

5. Which one of the following options correctly represents a thermodynamic process that is used as
a correction in the determination of the speed of sound in an ideal gas? (2017)
[A] (III) (iv) (R) [B] (I) (ii) (Q)
[C] (IV) (ii) (R) [D] (I) (iv) (Q)

Comprehension-III
In the figure a container is shown to have a movable (without friction) piston on top. The
container and the piston are all made of perfectly insulating material allowing no heat transfer
between outside and inside the container. The container is divided into two compartments by
a rigid partition made of a thermally conducting material that allows slow transfer of heat. The
lower compartment of the container is filled with 2 moles of an ideal monatomic gas at 700 K
and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. The heat
3 5
capacities per mole of an ideal monatomic gas are C V  R, CP  R, and those for an ideal
2 2
5 7
diatomic gas are C V  R, CP  R.
2 2

6. Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved,
the final temperature of the gases will be
(A) 550 K (B) 525 K
(C) 513K (D) 490 K (2014)

7. Now consider the partition to be free to move without friction so that the pressure of gases in both
compartments is the same. Then total work done by the gases till the time they achieve
equilibrium will be
(A) 250 R (B) 200 R
(C) 100 R (D) –100 R (2014)

Comprehension-IV

 5 P0
A small spherical monoatomic ideal gas bubble     is trapped
 3
Liquid
inside a liquid of density  (see figure). Assume that the bubble does
not exchange any heat with the liquid. The bubble contains n moles of H
gas. The temperature of the gas when the bubble is at the bottom is T0,
y
the height of the liquid is H and the atmospheric pressure is P0 (Neglect
surface tension).

8. As the bubble moves upwards, besides the buoyancy force the following forces are acting on it
(A) Only the force of gravity (2008)
(B) The force due to gravity and the force due to the pressure of the liquid
(C) The force due to gravity, the force due to the pressure of the liquid and the force due to
viscosity of the liquid
(D) The force due to gravity and the force due to viscosity of the liquid

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9. When the gas bubble is at a height y from the bottom, its temperature is (2008)
2/5 2/5
 P   gH   P    g(H  y) 
(A) T0  0  (B) T0  0 
 P0   gy   P0   gH 
3/5 3/5
 P   gH   P    g(H  y) 
(C) T0  0  (D) T0  0 
 P0   gy   P0   gH 

10. The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant) (2008)
(P   gH)2/5  nRgT0
(A) nRgT0 0 7/5
(B)
(P0   gy) (P0   gH) [P0   g(H  y)]3/5
2/5

(P0   gH)3/5  nRgT0

(C) nRgT0 8/5
(D) 3/5
(P0   gy) (P0   gH) [P0   g(H  y)]2/5

Comprehension-V

A fixed thermally conducting cylinder has a radius R and height L0. The cylinder is 2R
open at its bottom and has a small hole at its top. A piston of mass M is held at a
L
distance L from the top surface, as shown in the figure. The atmospheric pressure
is P0. L0
11. The piston is now pulled out slowly and held at a distance 2L from the
top. The pressure in the cylinder between its top and the piston will then
be
P Piston
(A) P0 (B) 0
2
P0 Mg P0 Mg
(C)  (D) 
2 R 2 2 R2 (2007)

12. While the piston is at a distance 2L from the top, the hole at the top is sealed. The piston is then
released, to a position where it can stay in equilibrium. In this condition, the distance of the piston
from the top is (2007)
 2P R 2  2
 P R  Mg 
(A)  2 0 (B)  0 2
 R P  Mg      2L 
2L
 R P
 0   0 
2
 P R  Mg   P R 2 
(C)  0   2L  (D)  20
 R P  Mg   
2L
 R2P
 0   0 

13. The piston is taken completely out of the cylinder. The hole at the top is
sealed. A water tank is brought below the cylinder and put in a position
so that the water surface in the tank is at the same level as the top of
L0
the cylinder as shown in the figure. The density of the water is . In
H
equilibrium, the height H of the water column in the cylinder satisfies
2
(A) g(L0H) + P0(L0  H) + L0P0 = 0
(B) g(L0H)2  P0(L0  H)  L0P0 = 0
(2007)
(C) g(L0H)2 + P0(L0  H)  L0P0 = 0
2
(D) g(L0H)  P0(L0  H) + L0P0 = 0

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MCQ-Multi Correct

1. A mixture of ideal gas contains 5 moles of monatomic gas and 1 mole of rigid diatomic gas is
initially at pressure P0, volume V0, and temperature T0. If the gas mixture is adiabatically
V
compressed to a volume 0 , then the correct statement(s) is /are, (Given 21.2 = 2.3; 23.2 = 9.2; R
4
is gas constant)
(A) Adiabatic constant of the gas mixture is 1.6
(B) The final pressure of the gas mixture after compression is in between 9P0 and 10P0
(C) The work |W| done during the process is 13RT0
(D) The average kinetic energy of the gas mixture after compression is in between 18RT0 and
19RT0. (2019)

2. One mole of a monatomic ideal gas goes through a V

thermodynamic cycle, as shown in the volume
versus temperature (V – T) diagram. The correct 3
statement(s) is/are: 2V0 2
[R is the gas constant]

V0 4 1

T
T0/2 T0 3T0/2 2T0
1
(A) Work done in this thermodynamic cycle (1  2  3  4  1) is W  RT0
2
Q12 5
(B) The ratio of heat transfer during processes 1  2 and 2  3 is 
Q 2 3 3
(C) The above thermodynamic cycle exhibits only isochoric and adiabatic processes.
Q12 1
(D) The ratio of heat transfer during processes 1  2 and 3  4 is  (2019)
Q3 4 2

3. One mole of a monatomic ideal gas undergoes a cyclic process T

as shown in the figure (where V is the volume and T is the
temperature). Which of the statements below is (are) true? II

I III

IV
V
(A) Process I is an isochoric process (B) In process II, gas absorbs heat
(C) In process IV, gas releases heat (D) Processes I and III are not isobaric (2018)

4. A flat plate is moving normal to its plane through a gas under the action of constant force F. The
gas is kept at a very low pressure. The speed of the plate v is much less than the average speed
u of the gas molecules. Which of the following options is/are true? (2017)
(A) The resistive force experienced by the plate is proportional to v
(B) The pressure difference between the leading and trailing faces of the plate is proportional to
uv
(C) The plate will continue to move with constant non-zero acceleration, at all times
(D) At a later time the external force F balances the resistive force.

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 97
5. A human body has a surface area of approximately 1 m 2. The normal body temperature is 10 K
above the surrounding room temperature T0. Take the room temperature to be T0 = 300 K. For
T0 = 300 K, and the value of  T04 =460 Wm-2 (where  is the Stefan-Boltzmann constant). Which
of the following option is/are correct? (2017)
(A) The amount of energy radiated by the body in 1 second is close to 60 Joules.
(B) If the surrounding temperature reduces by a small amount T0 <<T0, then to maintain the
same body temperature the same (living) human being needs to radiate W = 4 T03 T0 more
energy per unit time.
(C) Reducing the exposed surface area of the body (e.g by curling up) allows humans to maintain
the same body temperature while reducing the energy lost by radiation.
(D) If the body temperature rises significantly then the peak in the spectrum of electromagnetic
radiation emitted by the body would shift to longer wavelengths.

6. An incandescent bulb has a thin filament of tungsten that is heated to high temperature by
passing an electric current. The hot filament emits black-body radiation. The filament is observed
to break up at random locations after a sufficiently long time of operation due to non-uniform
evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the
following statement(s) is(are) true? (2016)
(A) The temperature distribution over the filament is uniform
(B) The resistance over small sections of the filament decreases with time
(C) The filament emits more light at higher band of frequencies before it breaks up
(D) The filament consumes less electrical power towards the end of the life of the bulb

7. An ideal monoatomic gas is confined in a horizontal

cylinder by a spring loaded piston (as shown in the
figure). Initially the gas is at temperature T1, pressure
P1 and volume V1 and the spring is in its relaxed state.
The gas is then heated very slowly to temperature T2,
pressure P2 and volume V2. During this process the
piston moves out by a distance x. Ignoring the friction (2015)
between the piston and the cylinder, the correct
statement(s) is(are)
1
(A) If V2 = 2V1 and T2 = 3T1, then the energy stored in the spring is P1V1
4
(B) If V2 = 2V1 and T2 = 3T1, then the change in internal energy is 3P1V1
7
(C) If V2 = 3V1 and T2 = 4T1, then the work done by the gas is P1V1
3
17
(D) If V2 = 3V1 and T2 = 4T1, then the heat supplied to the gas is P1V1
6

8. A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in
equilibrium at temperature T. Assuming the gases are ideal, the correct statement(s) is(are)
(A) The average energy per mole of the gas mixture is 2RT.
(B) The ratio of speed of sound in the gas mixture to that in helium gas is 6 / 5.
(C) The ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/2.
(D) The ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/ 2. (2015)

ARCHIVE-1920-JEE(Advanced)-PHYSICS
98
9. The figure shows the variation of specific
heat capacity (C) of a solid as a function of
temperature (T). The temperature is C
increased continuously from 0 to 500 K at a
constant rate. Ignoring any volume change,
the following statement(s) is (are) correct to 500
100 200 300 400
a reasonable approximation. T (K) (2013)
(A) the rate at which heat is absorbed in the range 0-100 K varies linearly with temperature T.
(B) heat absorbed in increasing the temperature from 0-100 K is less than the heat required for
increasing the temperature from 400 – 500 K.
(C) there is no change in the rate of heat absorption in range 400 – 500 K.
(D) the rate of heat absorption increases in the range 200 – 300 K.

0 1L 5L 6L
10. A composite block is made of slabs A, B, C, D and E heat
of different thermal conductivities (given in terms of a A B 3K E
1L
constant K) and sizes (given in terms of length, L) as
shown in the figure. All slabs are of same width. C 4K
6K
2K
Heat ‘Q’ flows only from left to right through the 3L
blocks. Then in steady state
D 5K
(A) heat flow through A and E slabs are same. 4L
(B) heat flow through slab E is maximum. (2011)
(C) temperature difference across slab E is smallest.
(D) heat flow through C = heat flow through B + heat flow through D.

11. One mole of an ideal gas in initial state A undergoes a cyclic V

process ABCA, as shown in the figure. Its pressure at A is P0. B
4V0
Choose the correct option(s) from the following
(A) Internal energies at A and B are the same A
V0 C
(B) Work done by the gas in process AB is P0V0 n 4
T0 T
P0
(C) Pressure at C is
4
T0
(D) Temperature at C is (2010)
4

12. Cv and Cp denote the molar specific heat capacities of a gas at constant volume and constant
pressure, respectively. Then
(A) Cp Cv is larger for a diatomic ideal gas than for a monoatomic ideal gas.
(B) Cp + Cv is larger for a diatomic ideal gas than for a monoatomic ideal gas.
(C) Cp/Cv is larger for a diatomic ideal gas than for a monoatomic ideal gas.
(D) Cp. Cv is larger for a diatomic ideal gas than for a monoatomic ideal gas. (2009)

13. The figure shows the P-V plot of an ideal gas taken through a P
A
cycle ABCDA. The part ABC is a semi-circle and CDA is half of an 3
ellipse. Then, 2 B
D
(A) the process during the path A  B is isothermal 1
C
(B) heat flows out of the gas during the path B  C  D
0
(C) work done during the path A  B  C is zero 1 2 3 V
(2009)
(D) positive work is done by the gas in the cycle ABCDA

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14. A bimetallic strip is formed out of two identical strips one of copper and the other of brass. The
coefficients of linear expansion of the two metals are c and B. On heating, the temperature of
the strip goes up by T and the strip bends to form an arc of radius of curvature R. Then R is
(A) proportional to T (B) inversely proportional to T (1999)
(C) proportional to | B - C| (D) inversely proportional to | B - C |

15. During the melting of a slab of ice at 273 K at atmospheric pressure,

(A) positive work is done by the ice-water system on the atmosphere
(B) positive work is done on the ice-water system by the atmosphere
(C) the internal energy of ice-water system increases
(D) the internal energy of the ice-water system decreases (1998)

16. Let v, vrms and v p respectively denote the mean speed, root mean square speed, and most
probable speed of the molecules in an ideal monatomic gas at absolute temperature T. The mass
of a molecule is m. Then
(A) no molecule can have a speed greater than 2 vrms
(B) no molecule can have speed less than v p/ 2
(C) vp < v < vrms
3
(D) the average kinetic energy of a molecule is mvp2 (1998)
4

17. Two bodies A and B have thermal emissivities of 0.01 and 0.81 respectively. The outer surface
areas of the two bodies are the same. The two bodies emit total radiant power at the same rate.
The wavelength B corresponding to maximum spectral radiance in the radiation from B is shifted
from the wavelength corresponding to maximum spectral radiance in the radiation from A by 1.00
m. If the temperature of A is 5802 K. (1994)
(A) the temperature of B is 1934 K (B) B = 1.5 m
(C) the temperature of B is 11604 K (D) the temperature of B is 2901 K

18. An ideal gas is taken from the state A (pressure P0, volume V0) to the state B (pressure P0/2,
volume 2V0) along a straight line path in the P-V diagram. Select the correct statement (s) from
the following. (1993)
(A) The work done by the gas in the process A to B exceeds the work that would be done by it if
the system were taken from A to B along the isotherm
(B) In the T-V diagram, the path AB becomes a part of the parabola.
(C) In the P-T diagram, the path AB becomes a part of hyperbola
(D) In going from A to B, the temperature T of the gas first increases to maximum value and then
decreases.

19. For an ideal gas:

(A) the change in internal energy in a constant pressure process from temperature T1 to T2 is
equal to nCv (T2T1), where Cv is the molar specific heat at constant volume and n is the
number of moles of the gas.
(B) the change in internal energy of the gas and the work done by the gas are equal in
magnitude in an adiabatic process.
(C) the internal energy does not change in an isothermal process.
(D) no heat is added or removed in an adiabatic process. (1989)

ARCHIVE-1920-JEE(Advanced)-PHYSICS
100
Match the Matrix

1. One mole of a monatomic ideal gas undergoes four P

thermodynamic processes as shown schematically in II
3P0
the PV-diagram below. Among these four processes,
one is isobaric, one is isochoric, one is isothermal and III
IV
one is adiabatic. Match the processes mentioned in I
List-1 with the corresponding statements in List-II. P0

V0 3V0 V
LIST–I LIST–II
P. In process I 1. Work done by the gas is zero
Q. In process II 2. Temperature of the gas remains unchanged
3. No heat is exchanged between the gas and its
R. In process III
surroundings
S. In process IV 4. Work done by the gas is 6P0V0
(A) P → 4; Q → 3; R → 1; S → 2 (2018)
(B) P → 1; Q → 3; R → 2; S → 4
(C) P → 3; Q → 4; R → 1; S → 2
(D) P → 3; Q → 4; R → 2; S → 1

P
2. One mole of mono-atomic ideal gas is taken along
two cyclic processes EFGE and F
32P0
EFHE as shown in the PV diagram. The
processes involved are purely isochoric, isobaric,
isothermal or adiabatic.

Match the paths in List I with the magnitudes of the

work done in List II and select the correct answer P0
E H
G

using the codes given below the lists.

V0 V

(2013)
List I List II
P. G  E 1. 160 P0V0 ln2
Q. G  H 2. 36 P0V0
R. F  H 3. 24 P0V0
S. F  G 4. 31 P0 V0
Codes:
P Q R S
(A) 4 3 2 1
(B) 4 3 1 2
(C) 3 1 2 4
(D) 1 3 2 4

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 101
3. One mole of a monatomic gas is taken P
B A
through a cycle ABCDA as shown in the P-V 3P
diagram. Column II give the characteristics
involved in the cycle. Match them with each
of the processes given in Column I. 1P
C D

0 1V 3V 9V V
(2011)
Column I Column II
(A) Process A  B (p) Internal energy decreases
(B) Process B  C (q) Internal energy increases.
(C) Process C  D (r) Heat is lost
(D) Process D  A (s) Heat is gained
(t) Work is done on the gas

4. Column I Contains a list of processes involving expansion of an ideal gas. Match this with
Column II describing the thermodynamic change during this process. Indicate your answer by
darkening the appropriate bubbles of the 4  4 matrix given in the ORS. (2008)
Column I Column II
(A) An insulated container has two chambers (p) The temperature of the
separated by a valve. Chamber I contains an gas decreases
ideal gas and the Chamber II has vacuum. The
valve is opened.
I II

ideal gas vacuum

(B) An ideal monoatomic gas expands to twice its (q) The temperature of the
1 gas increases or remains
original volume such that its pressure P  2 , constant
V
where V is the volume of the gas
(C) An ideal monoatomic gas expands to twice its (r) The gas loses heat
original volume such that its pressure P
1
 4/3 , where V is its volume
V
(D) An ideal monoatomic gas expands such that its (s) The gas gains heat
pressure P and volume V follows the behaviour
shown in the graph
P

V1 2V1 V

5. Column I gives some devices and Column II gives some process on which the functioning of
these devices depend. Match the devices in Column I with the processes in Column II and
indicate your answer by darkening appropriate bubbles in the 4  4 matrix given in the ORS.
(2007)
Column I Column II
(A) Bimetallic strip (p) Radiation from a hot body
(B) Steam engine (q) Energy conversion
(C) Incandescent lamp (r) Melting
(D) Electric fuse (s) Thermal expansion of solids

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102
6. Heat given to process is negative, match the P(atm)
following option of column I with the
corresponding option of column II J
Column I Column II 30
(A) JK (P) W > 0
(B) KL (Q) Q < 0
20 M
(C) LM (R) W < 0
(D) MJ (S) Q > 0
10 L
K

10 20 V(m3)

(2006)

Subjective

1. A liquid at 30°C is poured very slowly into a Calorimeter that is at temperature of 110°C. The
boiling temperature of the liquid is 80°C. It is found that the first 5 gm of the liquid completely
evaporates. After pouring another 80 gm of the liquid the equilibrium temperature is found to be
50°C. The ratio of the Latent heat of the liquid to its specific heat will be _____________°C.
[Neglect the heat exchange with surrounding] (2019)

2. Two conducting cylinders of equal length but

Insulating material
different radii are connected in series T1 T2
K1 K2
between two heat baths kept at
temperatures T1= 300 K and T2 = 100 K, as L
shown in the figure. The radius of the bigger L
cylinder is twice that of the smaller one and
the thermal conductivities of the materials of (2018)
the smaller and the larger cylinders are K1
and K2 respectively. If the temperature at the junction of the two cylinders in the steady state is
200 K, then K1 / K2 =__________.

3. One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume
becomes eight times its initial value. If the initial temperature of the gas is 100 K and the universal
gas constant R = 8.0 J mol1K1, the decrease in its internal energy, in Joule, is__________.
(2018)

4. A metal is heated in a furnace where a sensor is kept above the metal surface to read the power
radiated (P) by the metal. The sensor has a scale that displays log2 (P/P0), where P0 is a
constant. When the metal surface is at a temperature of 487°C, the sensor shows a value 1.
Assume that the emissivity of the metallic surface remains constant. What is the value displayed
by the sensor when the temperature of the metal surface is raised to 2767 °C? (2016)

5. Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and
A emits 104 times the power emitted from B. The ratio (A/B) of their wavelengths A and B at
which the peaks occur in their respective radiation curves is (2015)

ARCHIVE-1920-JEE(Advanced)-PHYSICS
 103
6. A thermodynamic system is taken from an initial state i
a
with internal energy Ui = 100 J to the final state f along two f
different paths iaf and ibf, as schematically shown in the P
figure. The work done by the system along the paths af, ib
and bf are W af = 200 J, W ib = 50 J and W bf = 100 J i b
respectively. The heat supplied to the system along the
path iaf, ib and bf are Qiaf , Qib and Qbf respectively. If the V
internal energy of the system in the state b is Ub = 200 J (2014)
and Qiaf = 500 J, the ratio Qbf / Qib is

7. Steel wire of lenght ‘L’ at 40C is suspended from the ceiling and then a mass ‘m’ is hung from its
free end. The wire is cooled down from 40C to 30C to regain its original length ‘L’. The
coefficient of linear thermal expansion of the steel is 105/C, Young’s modulus of steel is 1011
N/m2 and radius of the wire is 1 mm. Assume that L  diameter of the wire. Then the value of ‘m’
in kg is nearly (2011)

8. Two spherical bodies A (radius 6 cm ) and B(radius 18 cm ) are at temperature T1 and T2,
respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B
is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total
energy radiated by A to that of B? (2010)

9. A piece of ice (heat capacity = 2100 J kg-1 °C-1 and latent heat = 3.36 105J kg-1) of mass m
grams is at -5°C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting.
Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted.
Assuming there is no other heat exchange in the process, the value of m is (2010)

1
10. A diatomic ideal gas is compressed adiabatically to of its initial volume. If the initial
32
temperature of the gas is Ti (in Kelvin) and the final temperature is aTi, the value of a is (2010)

11. A metal rod AB of length 10x has its one end A in ice at 0C and the other end B in water at
100C. If a point P on the rod is maintained at 400C, then it is found that equal amounts of water
and ice evaporate and melt per unit time. The latent heat of evaporation of water is 540 cal/g and
latent heat of melting of ice is 80 cal/g. If the point P is at a distance of x from the ice end A, find
the value of . [Neglect any heat loss to the surrounding.] (2009)

12. In an insulated vessel, 0.05 kg steam at 373 K and 0.45 kg of ice at 253 K are mixed. Then, find
the final temperature of the mixture. (2006)
Given, Lfusion = 80 cal/g = 336 J/g, Lvaporization = 540 cal/g = 2268 J/g,
Sice = 2100 J/kg K = 0.5 cal/gK and Swater = 4200 J/kg K = 1 cal /gK

13. A cylinder of mass 1 kg is given heat of 20000J at atmospheric pressure. If initially temperature of
cylinder is 20C, find (2005)
(a) final temperature of the cylinder.
(b) work done by the cylinder.
(c) change in internal energy of the cylinder.
–1 0 –1
(Given that Specific heat capacity of cylinder= 400 J kg C , Coefficient of volume
–5 1 5 2
expansion = 910 C , Atmospheric pressure=10 N/m and Density of cylinder = 9000
3
kg/m )

ARCHIVE-1920-JEE(Advanced)-PHYSICS
104

Coeff. Of linear
14. A cubical block is floating inside a bath. The temperature of system is expn. = 
increased by small temperature T. It was found that the depth of
submerged portion of cube does not change. Find the relation between x
coefficient of linear expansion () of the cube and volume expansion of
Coeff. of volume
liquid (). expn. = 
(2004)

15. A uniform rod of length L, thermal conductivity K is

connected from one end to a furnace at temperature T1. Insulation
The other end of rod is at temperature T2 and is exposed
to atmosphere. The temperature of atmosphere is Ts. The Furnace
lateral part of rod is insulated. T1 A, K T2,  Ts
If T2 – Ts << Ts, T2 = Ts +  T & T  (T1 – Ts), find
proportionality constant of given equation. The heat loss to
atmosphere is through radiation only and the emissivity of (2004)
the rod is .

16. An ideal diatomic gas is enclosed in an insulated chamber at

Atmosphere
temperature 300 K. The chamber is closed by a freely movable
massless piston, whose initial height from the base is 1 m. Now the gas
is heated such that its temperature becomes 400 K at constant 1m
pressure. Find the new height of the piston from the base.If the gas is
compressed to initial position such that no exchange of heat
takes place, find the final temperature of the gas. (2004)

17. Hot oil is circulated through an insulated container with a T = 127

wooden lid at the top whose conductivity K = 0.149 J/(m-C,
thickness t = 5 mm, emissivity = 0.6. Temperature of the top of
the lid is maintained at T = 127C. If the ambient temperature Ta = 27C
T0
Ta = 27. Calculate Hot Oil
(i) rate of heat loss per unit area due to radiation from the lid.
(2003)
17
(ii) temperature of the oil. (Given    108 )
3

18. An insulated box containing monatomic ideal gas of molar mass M is moving with a uniform
speed v. The box suddenly stops and consequently the gas acquires a new temperature.
Calculate the change in the temperature of the gas. Neglect heat absorbed by the box. (2003)

2
19. A cubical box of side 1 meter contains helium gas (atomic weight 4) at a pressure of 100 N/m .
During an observation time of 1 second, an atom travelling with the root-mean-square speed
parallel to one of the edges of the cube, was found to make 500 hits with a particular wall, without
any collision with other atoms. (2002)
25
Take R = J/mol-K and k = 1.38  10-23 J/K
3
(a) Evaluate the temperature of the gas.
(b) Evaluate the average kinetic energy per atom.
(c) Evaluate the total mass of helium gas in the box.

ARCHIVE-1920-JEE(Advanced)-PHYSICS
 105
20. A monatomic ideal gas of two moles is taken through a cyclic D C
VD
process starting from A as shown in the figure. The volume
ratios are (VBVA) = 2 and (VDVA) = 4. If the temperature TA at V
A is 27C, calculate VB B
(a) The temperature of the gas at point B,
VA A
(b) heat absorbed or released by the gas in each process.
(c) The total work done by the gas during the complete cycle. O TA TB
T
Express your answer in terms of the gas constant R. (2001)

21. A 5 m long cylindrical steel wire with radius 2 x 103 m is suspended vertically from a rigid support
and carries a bob of mass 100 Kg at the other end. If the bob gets snapped, calculate the change
in temperature of the wire ignoring radiation losses.
(For the steel wire: Young’s Modulus = 2.1  1011 Pa; Density = 7860 Kg/m 3; Specific heat = 420
J/Kg-K) (2001)

22. An ice cube of mass 0.1 Kg at 00C is placed in an isolated container which is at 2270C. The
specific heat S of the container varies with temperature T according to the empirical relation S =
A+BT, where A = 100 cal/Kg-K and B = 2 x 102 cal/Kg-K2. If the final temperature of the container
is 270C, determine the mass of the container.
(Latent heat of fusion for water = 8 x 104 cal/Kg-K, Specific heat of water = 103 cal/Kg-K) (2001)
P
23. Two moles of an ideal monoatomic gas is taken through a cycle ABCA
B
as shown in the P-T diagram. During the process AB, pressure and 2P1 C
temperature of the gas vary such that PT = constant. If T1 = 300 K,
calculate
(a) The work done on the gas in the process AB and P1 A
(b) The heat absorbed or released by the gas in each of the
T1 2T1
processes. T

Give answers in terms of the gas constant R. (2000)

24. Two moles of an ideal monoatomic gas, initially at pressure P1 and volume V1 undergo an
adiabatic compression until its volume is V2. Then the gas is given heat Q at constant volume V2.
(a) Sketch the complete process on a p-V diagram
(b) Find the total work done by the gas, the total change in its internal energy and the final
temperature of the gas.[Give your answers in terms of P1, V1, V2 Q and R]. (1999)

25. A solid body X of heat capacity C is kept in an atmosphere whose temperature is

TA = 300 K. At time t = 0 the temperature of X is T0 = 400 K. It cools according to Newton’s law of
cooling. At time t1, its temperature is found to be 350 K.
At this time (t1), the body X is connected to a large body Y at atmospheric temperature TA,
through a conducting rod of length L, cross-sectional area A and thermal conductivity K. The heat
capacity of Y is so large that any variation in its temperature may be neglected. The cross-
sectional area A of the connecting rod is small compared to the surface area of X. Find the
temperature of X at time t = 3t1. (1998)

26. One mole of an ideal monatomic gas is taken round the cyclic P
process ABCA as shown in the figure. Calculate 3Po
B
(a) the work done by the gas
(b) the heat rejected by the gas in the path CA and the heat C
Po A
absorbed by the gas in the path AB;
(c) the net heat absorbed by the gas in the path BC; Vo 2Vo V
(d) the maximum temperature attained by the gas during the cycle. (1998)

ARCHIVE-1920-JEE(Advanced)-PHYSICS
106
27. A sample of 2 kg of monoatomic Helium (assume ideal) is taken through the process ABC and
another sample of 2 kg of the same gas is taken through the process ADC. Given, relative
molecular mass of Helium = 4.
(i) What is the temperature of Helium in each of the states A, B, C and D?
P
(ii) Is there any way of telling afterwards which
B
sample of Helium went through the process (104 N/m2) 10 C

ABC and which went through the process ADC?

5 D
Write yes or No. A

(iii) How much is the heat involved in each of the V(m3)

10 20 (1997)
processes ABC and ADC?

28. A double pane window used for insulating a room thermally from outside, consists of two glass
2
sheets each of area 1 m and thickness 0.01 m separated by a 0.05 m thick segment air space.
In the steady state the room glass interface and the glass outdoor interface are at constant
temperature of 27C and 0C respectively. Calculate the rate of heat flow through the window
pane. Also find the temperature of other interfaces. Given thermal conductivities of glass and air
are as 0.8 and 0.08 Wm-1K-1 respectively. (1997)

29. A thin rod of negligible mass and area of cross-section 4  106 m2, suspended vertically from one
end, has a length of 0.5 m at 100C. The rod is cooled to 0C, but prevented from contracting by
attaching a mass at the lower end. Find (i) this mass, and (ii) the energy stored in the rod. Given
for the rod, Young’s modulus = 1011 N/m2, coefficient of linear expansion 105 K1 and g = 10 m/s2
(1997)

30. The apparatus shown in the figure consists of four glass

columns connected by horizontal sections. The height of
two central columns B and C are 49 cm each. The two
outer columns A and D are open to the atmosphere. A B C D
and C are maintained at a temperature of 95C while A 50 c 0
95 c
0
95 c 50 c
the columns B and D are maintained at 5C. The height (1997)
of the liquid in A and D measured from the base line are
52.8 cm and 51 cm respectively. Determine the
coefficient of thermal expansion of the liquid.

31. One mole of a diatomic ideal gas ( = 1.4) is taken through a cyclic process starting from point A.
The process A  B is an adiabatic compression, B  C is an isobaric expansion C  D is an
adiabatic expansion and D  A is an isochoric process. The volume ratios are
VA/VB = 16 and VC/VB = 2 and the temperature at A is TA = 300 K. Calculate the temperature of
the gas at the points B and D and find the efficiency of the cycle. (1997)

32. The temperature of 100 g of water is to be raised form 24C to 90C by adding steam to it.
Calculate the mass of the steam required for this purpose. (1996)

33. At 27C two moles of an ideal monoatomic gas occupy a volume V. The gas expands
adiabatically to a volume 2V. Calculate (i) the final temperature of the gas,(ii) change in its
internal energy, and (iii) the work done by the gas during this process. (1996)

ARCHIVE-1920-JEE(Advanced)-PHYSICS
 107

34. A gaseous mixture enclosed in a vessel of volume V consists of one mole of gas A with
 (=CP/CV) = 5/3 and another gas B with  = 7/5 at a certain temperature T. The relative molar
masses of the gas A and B are 4 and 32, respectively. The gases A and B do not react with each
19/13
other and are assumed to be ideal. The gaseous mixture follows the equation PV = constant,
in adiabatic processes.
(a) Find the number of moles of the gas B in the gaseous mixture.
(b) Compute the speed of sound in the gaseous mixture at T = 300 K.
(c) If T is raised by 1 K from 300 K, find the percentage change in the speed of sound in the
gaseous mixture.
(d) The mixture is compressed adiabatically to 1/5 of its initial volume V. Find the change in its
adiabatic compressibility in terms of the given quantities. (1995)

35. A closed container of volume 0.02 m 3 contains a mixture of neon and argon gases, at a
temperature of 27C and pressure of 1105 N/m2. The total mass of the mixture is 28 gm. If the
gram molecular weights of neon and argon are 20 and 40 respectively, find the masses of the
individual gases in container, assuming them to be ideal. (Universal gas constant R = 8.314
J/mol. K) (1994)

36. An ideal gas is taken through a cyclic thermodynamic process through four steps. The amounts of
heat involved in these steps are Q1 = 5960 J, Q2 = -5585 J, Q3 = -2980 J and Q4 = 3645 J
respectively. The corresponding works involved are W 1 = 2200 J, W 2 = -825J, W 3 = 1100 J and
W 4 respectively.
(i) Find the value of W 4.
(ii) What is the efficiency of the cycle? (1994)

y
37. One mole of a monatomic ideal gas is taken through the cycle shown A
in the figure: AB: adiabatic expansion B
B  C: cooling at constant volume
C  D : adiabatic compression P D

D  A : heating at constant volume. C

The pressure and temperature at A, B, etc. are denoted by PA, PB, O V x

etc. TA, TB etc. respectively. Given that

TA  1000K,PB   2 / 3  PA and PC = (1/3) PA.
Calculate the following quantities:
(i) The work done by the gas in process A  B
(ii) The heat lost by the gas in process B  C
2/5
 2
(iii) The temperature TD [Given:   = 0.85] (1993)
3

38. A cylindrical block of length 0.4 m and area of cross-section 0.04 m 2 is placed coaxially on a thin
metal disc of mass 0.4 Kg and the same cross-section. The upper face of the cylinder is
maintained at a constant temperature of 400 K and the initial temperature of the disc is 300 K. If
the thermal conductivity of the material of the cylinder is 10 watt/m-K and the specific heat of the
material of the disc is 600 J/kg.K, how long will it take for the temperature of the disc to increase
to 350 K? Assume, for purposes of calculation, the thermal conductivity of the disc to be very high
and the system to be thermally insulated except for the upper face of the cylinder. (1992)

ARCHIVE-1920-JEE(Advanced)-PHYSICS
108
39. Two moles of helium gas undergo a cyclic process as A B
2 atm
shown in Figure. Assuming the gas to be ideal,
calculate the following quantities in this process
(a) The net change in the heat energy 1 atm C
D
(b) The net work done
(c) The net change in internal energy.
300K 400K
(1992)

 7 
40. Three moles of an ideal gas  CP  R  at pressure PA and temperature TA is isothermally
 2 
expanded to twice its initial volume. It is then compressed at constant pressure to its original
volume. Finally gas is heated at constant volume to its original pressure PA.
(a) Sketch P-V and P-T diagrams for the complete process.
(b) Calculate the net work done by the gas, and net heat supplied to the gas during the complete
process. (1991)

41. An ideal gas having initial pressures P, volume V and temperature T is allowed to expand
adiabatically until its volume becomes 5.66 V while its temperature falls to T/2.
(a) How many degrees of freedom do the gas molecules have?
(b) Obtain the work done by the gas during the expansion as a function of initial pressure P and
volume V. (1990)

Temperature
42. A solid material is supplied with heat at a constant rate. The
E
temperature of the material is changing with the heat input as C D
shown in the graph. Study the graph carefully and answer the
A B
following questions:
(i) What do the horizontal regions AB and CD represent?
(ii) If CD is equal to 2AB, what do you infer? O Heat input
(1990)
(iii) What does the slope of DE represent?
(iv) the slope of OA > the slope of BC. What does this indicate?

43. An ideal monoatomic gas is confined in a cylinder by a Open

spring loaded piston of cross section 8.010 -3 m2 . atmosphere
Initially the gas is at 300 K and occupies a volume of Heater
2 . 4  1 0 - 3 m 3 a n d t h e sp ri n g i s i n i t s re l ax ed
Rigid
(unscratched, uncompressed) state as shown in the Support
figure. The gas is heated by a small electric heater until
the piston moves out slowly by 0.1 m. Calculate the
final temperature of the gas and the heat supplied (in Joules) by the heater. The force constant of
5 -2
the spring is 8000 N/m and atmospheric pressure is 1.010 Nm . The cylinder and the piston
are thermally insulated. The piston is massless and there is no friction between the piston and the
cylinder. Neglect heat loss through the lead wires of the heater. The heat capacity of the heater
coil is negligible. Assume the spring to be massless. (1989)

44. Two moles of helium gas ( = 5/3) are initially at a temperature of 27C and occupy a volume of 20
litres. The gas is first expanded at constant pressure until the volume is doubled. It then undergoes an
adiabatic change until the temperature returns to its initial value.
(a) Sketch the process on a P-V diagram.
(b) What are the final volume and pressure of the gas?
(c) What is the work done by the gas? (1988)

45. An ideal gas has a specific heat capacity at constant pressure CP = 5R/2. The gas is kept in a
closed vessel of volume 0.0083 m 3, at a temperature of 300 K and a pressure of 1.6  106 N/m2.
An amount of 2.49  104 Joule of heat energy is applied to the gas. Calculate the final
temperature and pressure of the gas. (1987)

ARCHIVE-1920-JEE(Advanced)-PHYSICS
 109
46. A thin tube of uniform cross section is sealed at both ends. It lies horizontally, the middle 5 cm
containing mercury and the two equal ends containing air at the same pressure P. When the tube
is held at an angle 60 with the vertical direction, the length of the air column above and below
the mercury column are 46 cm and 44.5 cm respectively. Calculate the pressure P in cm of
mercury. (The temperature of the system is kept at 30C) (1986)

47. An electric heater is used in a room of total wall area 137 m 2 to maintain a temperature of +20C
inside it, when the outside temperature is -10C. The walls have three different layers materials.
The inner most layer is of wood thickness 2.5 cm, the middle layer is of cement of thickness 1.0
cm and the outer most layer is of brick of thickness 25.0 cm. Find the power of the electric heater.
Assume that there is no heat loss through the floor and the ceiling. The thermal conductivities of
wood, cement and brick are 0.125, 1.5 and 1.0 watt/m/C respectively. (1986)

48. Two glass bulbs of equal volume are connected by a narrow tube and are filled with a gas at 0C
and a pressure of 76 cm of mercury. One of the bulbs is then placed in melting ice and the other is
placed in a water bath maintained at 62C. What is the new value of the pressure inside the bulbs?
The volume of the connecting tube is negligible. (1985)

49. The rectangular box shown in the figure has a partition which can
slide without friction along the length of the box. Initially each of the
two chambers of the box has one mole of a monoatomic ideal gas
( = 5/3) at a pressure P0, volume V0 and temperature T0.
The chamber on the left is slowly heated by an electric heater. The walls of the box and the
partition are thermally insulated. Heat loss through the lead wires of the heater is negligible. The
gas in the left chamber expands pushing the partition until the final pressure in both chambers
becomes 243P0/32. Determine (i) the final temperature of the gas in each chamber and (ii) the
work done by the gas in the right chamber. (1984)

50. (a) One mole of oxygen at 270C and at one atmospheric pressure is enclosed in a vessel.
(i) Assuming the molecules to be moving with Vrms. Find the number of collisions per second
which the molecules make with 1 m2 area of the vessel wall.
(ii) The vessel is now thermally insulated and moved with a constant speed V0. It is then suddenly
0
stopped. The process results in a rise of the temperature of the gas by 1 C. Calculate the
speed V0. (1983)

51. A solid sphere of copper of radius R and hollow sphere of the same material of inner radius r and
outer radius R are heated to the same temperature and allowed to cool in the same environment.
Which of them starts cooling faster? (1982)

52. Calculate the work done when one mole of a perfect gas is compressed adiabatically. The initial
pressure and volume of the gas are 105 N/m2 and 6 litres respectively. The final volume of the
gas is 2 litres. Molar specific heat of the gas at constant volume is 3R/2. (1982)

53. An ideal gas is enclosed in a vertical cylindrical container and supports a freely moving piston of
mass M. The piston and the cylinder have equal cross-sectional area A. Atmospheric pressure is
p0, and when the piston is in equilibrium, the volume of the gas is V0. The piston is now displaced
slightly from its equilibrium position. Assuming that the system is completely isolated from its
surroundings, show that the piston executes simple harmonic motion and find the frequency of
oscillations. (1981)

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54. A cyclic process ABCA shown in the V-T diagram is V

C B
performed with constant mass of an ideal gas. Show the V2
same process on a P-V diagram. (In the figure, CA is
parallel to the v-axis and BC is parallel to the T-axis.)

V1
A
T
T1 T2 (1981)

55. A lead bullet just melts when stopped by an obstacle. Assuming that 25 percent of the heat is
absorbed by the obstacle, find the speed of the bullet if its initial temperature is 27C. (Melting
point of lead = 327C, specific heat of lead = 0.03 cal/gm/C, latent heat of fusion of lead = 6
calories/gm, J = 4.2 joules/calorie) (1981)

56. A jar contains a gas and a few drops of water at TK. The pressure in the jar is 830 mm of Hg. The
temperature of the jar is reduced by 1%. The saturated vapour pressure of water at the two
temperatures are 30 and 25 mm of Hg. Calculate the new pressure in the jar. (1980)

ARCHIVE-1920-JEE(Advanced)-PHYSICS