2-HEAT AND THERMODYNAMICS

GENERAL INSTRUCTIONS
1. This Question Paper contains 30 objective type questions.
2. Each question has 4 choices (A), (B), (C) and (D), out of which only one is correct.
3. For each question, you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer
is given. In all other cases, minus one (–1) Mark will be awarded.
Duration : 1 Hour Max. Marks : 90
Straight Objective Type
This section contains 30 Single choice questions. Each question has choices (A), (B), (C) and (D), out of
which ONLY ONE is correct.
1. 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) 4 R T (B) 5 R T (C) 15 R T (D) 11 R T
2. Maxwell’s velocity distribution curve is given for two different
temperatures. For the given curves.
(A) T1 > T2 (B) T1 < T2
(C) T1  T2 (D) T1 = T2
3. The ratio of translational and rotational kinetic energies at 100 K temperature is 3 : 2. Then the internal
energy of one mole gas at that temperature is[R = 8.3 J/mol-K]
(A) 1175J (B) 1037.5 J (C) 2075 J (D) 4150J
4. 12 gm He and 4 gm H2
is filled in a container of volume 20 litre maintained at temperature
300 K. The pressure of the mixture is nearly :
(A) 3 atm (B) 5 atm (C) 6.25 atm (D) 12.5 atm
5. Which of the following will have maximum total kinetic energy at temperature 300 K.
(A) 1 kg H2
(B) 1 kg He
(C)
2
1
kg H2
+
2
1
kg He (D)
4
1
kg H2
+
4
3
kg He
6. A ring shaped tube contains two ideal gases with equal masses and
atomic mass numbers M1 = 32 and M2 = 28. The gases are separated
by one fixed partition P and another movable conducting partition S which
can move freely without friction inside the ring. The angle  as shown in
the figure in equilibrium is:
(A)
8
7
(B)
7
8
(C)
16
15
(D)
15
16
PART TEST - 1 (PT-1)
TOPIC : HEAT AND THERMODYNAMICS (PHYSICS)

7. In an experiment the speeds of any five molecules of an ideal gas are recorded. The experiment is
repeated N times where N is very large. The average of recorded values, is :
(A)
M
RT
2
(B) M
RT
8
 (C)
M
RT
3
(D)
M
RT
8. Temperature at which Fahrenheit and Kelvin pair of scales give the same reading will be:
(A)  = –40 (B)  = 40 (C)  = 574.25 (D) 512.45
9. 20 gm ice at –10 ºC is mixed with m gm steam at 100 ºC. The minimum value of m so that finally all ice and
steam converts into water is : (Use sice=0.5 cal/gmºC,swater =1 cal/gmºC,L (melting)=80 cal/gm and L
(vaporization)=540 cal/gm)
(A)
27
185
gm (B)
17
135
gm (C)
32
85
gm (D)
17
113
gm
10. An ice block at 0°C is dropped from height ‘h’ above the ground. What should be the value of ‘h’ so that
it melts completely by the time it reaches the bottom assuming the loss of whole gravitational potential
energy is used as heat by the ice ? [Given : Lf
= 80 cal/gm]
(A) 33.6 m (B) 33.6 km (C) 8 m (D) 8 km
11. n moles of a gas filled in a container at temperature T is in
thermodynamic equilibrium initially. If the gas is compressed slowly
and isothermally to half its initial volume the work done by the
atmosphere on the piston is:
(A)
nRT
2
(B) 
nRT
2
(C) n R T n 2
1
2






 (D)  n R T n 2
12. In a process the pressure of an ideal gas is proportional to square of the volume of the gas. If the
temperature of the gas increases in this process, then work done by this gas:
(A) is positive (B) is negative
(C) is zero (D) may be positive
13. A vessel contains an ideal monoatomic gas which expands at constant pressure, when heat Q is given
to it. Then the work done in expansion is:
(A) Q (B)
3
5
Q (C)
2
5
Q (D)
2
3
Q
14. 5 moles of Nitrogen gas is enclosed in an adiabatic cylindrical vessel.
The piston itself is a rigid light cylindrical container containing 3 moles
of Helium gas. There is a heater which gives out a power 100 cal/sec
to the nitrogen gas. A power of 30 cal /sec is transferred to Helium
through the bottom surface of the piston. The rate of increment of
temperature of the nitrogen gas assuming that the piston moves slowly:
(A) 2 K/sec (B) 4 K/sec
(C) 6 K/sec (D) 8 K/sec
15. The gas law
T
PV
= constant for a given amount of a gas is true for :
(A) isothermal change only. (B) adiabatic change only.
(C) both isothermal & adiabatic changes. (D) neither isothermal nor adiabatic change.

16. All the rods have same conductance ‘K’ and same area of cross section
S. If endsA and C are maintained at temperature 2T0
and T0
respectively
then which of the following is/are correct:
(A) Rate of heat flow through ABC, AOC and ADC is same
(B) Rate of heat flow through BO and OD is not same
(C) Total Rate of heat flow from A to C is
a
2
T
S
K
3 0
(D) Temperature at junctions B, O and D are same
17. A hollow copper sphere and a hollow copper cube, of same surface area and negligible thickness, are
filled with warm water of same temperature and placed in an enclosure of constant temperature, a few
degrees below that of the bodies. Then in the beginning :
(A) the rate of energy lost by the sphere is greater than that by the cube
(B) the rate of fall of temperature for sphere is greater than that for the cube.
(C) the rate of energy lost by the sphere is less than that by the cube
(D) the rate of fall of temperature for sphere is less than that for the cube.
18. The colour of a star indicates its :
(A) weight (B) size (C) temperature (D) distance
19. Two identical solid spheres have the same temperature. One of the sphere is cut into two identical pieces.
The intact sphere radiates an energy Q during a given small time interval. During the same interval, the two
hemispheres radiate a total energy Q'. The ratio Q'/Q is equal to :
(A) 2.0 (B) 4.0 (C)
3
2
(D) 1.5
20. A calorimeter contains 50 g of water at 50°C. The temperature falls to 45°C in 10 minutes. When the
calorimeter contains 100 g of water at 50°C, it takes 18 minutes for the temperature to become 45°C. then
the water equivalent of the calorimeter is :
(A) 12.5 g (B) 6.25 g (C) 25 g (D) 15 g
21. Heat is flowing through two cylindrical rods made of same materials whose ends are maintained at similar
temperatures. If diameters of the rods are in ratio 1 : 2 and lengths in ratio 2 : 1, then the ratio of thermal
current through them in steady state is :
(A) 1 : 8 (B) 1 : 4 (C) 1 : 6 (D) 4 : 1
22. A balloon containing an ideal gas has a volume of 10 litre and temperature of 17ºC. If it is heated slowly to
75ºC, the work done by the gas inside the balloon is (neglect elasticity of the balloon and take atmospheric
pressure as 105
Pa)
(A) 100 J (B) 200 J
(C) 250 J (D) data insufficient
23. In the PV diagram shown. The gas does 5 J of work in isothermal
process a b and 4 J in adiabatic process b c. What will be the change
in internal
energy of the gas in straight path c to a?
(A) 9 J (B) 1 J
(C) 4 J (D) 5 J
24. A monoatomic ideal gas is filled in a nonconducting container. The gas can be compressed by a
movable nonconducting piston. The gas is compressed slowly to 12.5% of its initial volume. The
percentage increase in the temperature of the gas is
(A) 400% (B) 300%
(C) – 87.5% (D) 0%

25. A diatomic ideal gas is heated at constant volume until the pressure is doubled and again heated at
constant pressure until volume is doubled. The average molar heat capacity for whole process is:
(A)
6
R
13
(B)
6
R
19
(C)
6
R
23
(D)
6
R
17
26. The ratio of final root mean square velocity to initial root mean square velocity of nitrogen molecules if
nitrogen gas is compressed adiabatically from a pressure of one atmosphere to a pressure of
two atmosphere is :
(A) 22/7
(B) 21/7
(C) 21/5
(D) 22/5
27. Four particles have velocities 1, 0, 2, 3 m/s. The root mean square velocity of the particles is: (in m/s)
(A) 3.5 (B) 5
.
3 (C) 1.5 (D)
3
14
28. V–T diagram for a process of a given mass of ideal gas is as shown
in the figure. During the process pressure of gas.
(A) first increases then decreases
(B) continuously decreases
(C) continuously increases
(D) first decreases then increases.
29. A slab X of thickness ‘t’, thermal conductivity ‘K’ and area of cross-section ‘A’ is placed in thermal contact
with another slab Y which is 2n2
times thicker,4n times conductive and having n times larger cross section
area. If the outside face of X is maintained at 100°C, the outside face of Y at 0°C,then the temperature of the
junction  is represented by the graph (n > 0) :
(A) (B)
(C) (D)
30. Two conducting movable smooth pistons are kept inside a non
conducting, adiabatic container with initial positions as shown. Gas is
present in the three parts A, B & C having initial pressures as shown.
Now the pistons are released. Then the final equilibrium position length
of part A will be
(A)
8
L
(B)
4
L
(C)
6
L
(D)
5
L

Answers
1. (D) 2. (B) 3. (C) 4. (C) 5. (A) 6. (D)
7. (A) 8. (C) 9. (C) 10. (B) 11. (A) 12. (A)
13. (C) 14. (A) 15. (C) 16. (D) 17. (D) 18. (C)
19. (D) 20. (A) 21. (A) 22. (B) 23. (C) 24. (B)
25. (B) 26. (B) 27. (B) 28. (B) 29. (A) 30. (B)

1. This Question Paper contains 24 questions.
2. For each question in Section I , you will be awarded 3 Marks if you give the correct answer and zero
Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded.
3. For each question in Section II , you will be awarded 4 Marks if you give the correct answer. There is
no negative marking.
4. For each question in Section III, you will be awarded 3 Marks if you give the correct answer and zero
5. For each question in Section IV, you will be awarded 4 Marks if you give the correct answer and zero
6. For each question in Section V, you will be awarded 6 Marks if you give ALL the correct answer(s) or
awarded :
(i) 1 Mark for correct answer in one row.
(ii) 2 Marks for correct answer in two rows.
(iii) 4 Marks for correct answer in three rows.
SECTION - I
1. A piston can freely move inside a horizontal cylinder closed from both ends. Initially, the piston separates
the inside space of the cylinder into two equal parts each of volume V0
, in which an ideal gas is
contained under the same pressure p0
and at the same temperature. What work has to be performed in
order to increase isothermally the volume of one part of gas 2 times compared to that of the other by
slowly moving the piston ?
(A) p0
V0
(B) 2p0
V0
(C) p0
V0
n
8
9
(D) p0
V0
n2
2. A uniform pressure P is exerted by an external agent on all sides of a solid cube at temperature t ºC.
By what amount should the temperature of the cube be raised in order to bring its volume back to its
original volume before the pressure was applied if the bulk modulus is B and co-efficient of volumetric
expansion is ?
(A) P/B (B) P/B (C) B/P (D) 1/BP
3. Two rodsof same dimensions, but made of different materials are joined end to end with their free endsbeing
maintained at 100ºC and 0ºC respectively. The temperature of the junction is 70ºC. Then the temperature of
the junction if the rods are interchanged will be equal to :
(A) 10ºC (B) 30ºC (C) 90ºC (D) 40ºC
4. Assume a sample of an ideal gas in a vessel. Where velocity of molecules are between 2 m/sec to
5 m/sec and velocity of molecules (v) and number of molecules (n) are related as n = 7v – v2
– 10. The most
probable velocity in sample is. Where v is measured in m/sec.
(A) 3.5 m/sec (B) 5 m/sec (C) 10 m/sec (D) 4 m/sec

5. If specific heat capacity of a substance in solid and liquid state is proportional to temperature of the substance,
then if heat is supplied to the solid initially at – 20°C (having melting point 0°C) at constant rate. Then the
temperature dependence of substance with time will be best represented by :
(A) (B)
(C) (D)
6. In the figure shown the pressure of the gas in state B is:
(A)
25
63
P0 (B)
25
73
P0
(C)
25
48
P0 (D) none of these
7. A hot black body emits the energy at the rate of 16 J m–2
s–1
and its most intense radiation corresponds
to 20,000 Å. When the temperature of this body is further increased and its most intense radiation
corresponds to 10,000 Å, then the energy radiated in Jm–2
s–1
will be :
(A) 4 (B) 1 (C) 64 (D) 256
8. Two identical rectangular rodsof metal are welded end to end in seriesbetween
temperature 0°C and 100°C and 10 J of heat is conducted (in steady state
process) through the rod in 2.00 min. If 5 such rods are taken and joined as
shown in figure maintaining the same temperature difference betweenA and
B, then the time in which 20 J heat will flow through the rods is :
(A) 30 sec. (B) 2 min. (C) 3 min. (D) 60 sec.
SECTION - II
Multiple Correct Answers Type
This section contains 4 Multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out
of which ONE OR MORE may be correct.
9. An ideal gas undergoes a cyclic process abcda which is
shown by pressure- density curve.
P

d
a
b
c
1 2
(A) Work done by the gas in the process 'bc' is zero
(B) Work done by the gas in the process 'cd' is negative
(C) Internal energy of the gas at point 'a' is greater than at state 'c'
(D) Net work done by the gas in the cycle is negative.

10. The emissive power of a black body at T = 300 K is 100 Watt/m2
. Consider a body B of area A = 10 m2
coefficient of reflectivity r = 0.3 and coefficient of transmission t = 0.5 and at temperature 300 K. Then
which of the following is correct :
(A) The emissive power of B is 20 W/m2
(B) The emissive power of B is 200 W/m2
(C) The power emitted by B is 200 Watts (D) The emissivity of B is = 0.2
11. The ends of a rod of uniform thermal conductivity are maintained at different (constant) temperatures. After
the steady state is achieved :
(A) heat flows in the rod from high temperature to low temperature even if the rod has nonuniform cross
sectional area.
(B) temperature gradient along length is same even if the rod has non uniform cross sectional area.
(C) heat current is same even if the rod has non-uniform cross sectional area.
(D) if the rod has uniform cross sectional area the temperature is same at all points of the rod.
12. Number of collisions of molecules of a gas on the wall of a container per m2 will :
(A) Increase if temperature and volume both are doubled.
(B) Increase if temperature and volume both are halved.
(C) Increase if pressure and temperature both are doubled.
(D) Increase if pressure and temperature both are halved.
SECTION - III
Reasoning Type
This section contains 4 Reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out
of which ONLY ONE is correct.
13. Statement -1 : It is possible for both the pressure and volume of a monoatomic ideal gas of a given
amount to change simultaneously without causing the internal energy of the gas to change.
Statement-2: The internal energy of an ideal gas of a given amount remains constant if temperature
does not change. It is possible to have a process in which pressure and volume are changed such
that temperature remains constant.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(B) Statement-1 isTrue, Statement-2 isTrue; 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
14. Statement-1 : Molar heat capacity of an ideal monoatomic gas at constant volume is a constant at all
temperatures.
Statement-2 : As the temperature of an monoatomic ideal gas is increased, number of degrees of freedom
of gas molecules remains constant.
(A) Statement-1 isTrue, Statement-2 isTrue; 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
(D) Statement-1 is False, Statement-2 is True.
15. Statement-1 : Burns sustained from steam at 100o
C are usually more serious than those sustained by
boiling water (at 100o
C)
Statement-2 : To convert 1gm of water at 100o
C to 1 gm of steam at 100o
C, 540 calories of heat is to be
supplied. Hence 1gm of steam at 100o
C has more heat content than 1 gm of water at 100o
C
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(B) Statement-1 isTrue, Statement-2 isTrue; Statement-2 is NOT a correct explanation for Statement-1
(D) Statement-1 is False, Statement-2 is True

16. Statement-1 : If the absolute temperature of a gas is doubled, the final rms-velocity of the gas particles
becomes 2 times the initial value.
Statement-2: The average translational kinetic energy of molecules in a gas is equal to both
2
1
mvrms
2
and
2
3
kT.( where vrms
, k and T have usual meanings)
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
SECTION - IV
Comprehension Type
This section contains 2 Paragraphs. Based upon each paragraph, 3 Multiple choice questions have
to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
Comprehension (For Q.No. 17 to 19)
A 0.60 kg sample of water and a sample of ice are placed in two compartments A and B that are
separated by a conducting wall, in a thermally insulated container. The rate of heat transfer from the
water to the ice through the conducting wall is constant P, until thermal equilibrium is reached. The
temperature T of the liquid water and the ice are given in graph as functions of time t. Temperature of
the each compartment remain homogeneous during whole heat transfer process.
Given specific heat of ice = 2100 J/kg-K
Given specific heat of water = 4200 J/kg-K
Latent heat of fusion of ice = 3.3 × 105 J/kg
17. The value of rate P is
(A) 42.0 W (B) 36.0 W (C) 21.0 W (D) 18.0 W
18. The initial mass of the ice in the container is equal to
(A) 0.36 kg (B) 1.2 kg (C) 2.4 kg (D) 3.6 kg
19. The massof the ice formed due to conversion from the water till thermal equilibrium isreached, isequal to
(A) 0.12 kg (B) 0.15 kg (C) 0.25 kg (D) 0.40 kg
Comprehension (For Q.No. 20 to 22)
A quantity of an ideal monoatomic gas consists of n moles initially at temperature T1. The pressure and
volume both are then slowly doubled in such a manner so as to trace out a straight line on a P-V
diagram.
20. For this process, the ratio
1
nRT
W
is equal to (where W is work done by the gas) :
(A) 1.5 (B) 3 (C) 4.5 (D) 6

21. For the same process, the ratio
1
nRT
Q
is equal to (where Q is heat supplied to the gas) :
(A) 1.5 (B) 3 (C) 4.5 (D) 6
22. If C is defined as the average molar specific heat for the process then
R
C
has value
(A) 1.5 (B) 2 (C) 3 (D) 6
SECTION - IV
Matrix - Match Type
This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column-I
and four or five statements (p,q,r, s or p,q,r, s,t) in Column-II. Any given statement in Column-I can have
correct matching with ONE OR MORE statement(s) in Column-II. The answers to these questions have to
be appropriately marked as illustrated in the following example. If the correct matches are A-p, A-r, B-p,
B-s, C-r, C-s, D-q and D-t then the answer should be written as : A  p,r ; B p, s ; C  r, s ; D  q, t.
23. A sample of gas goes from state A to state B in four different manners, as shown by the graphs. Let W
be the work done by the gas and U be change in internal energy along the path AB. Correctly match
the graphs with the statements provided.
Column  Column 
(A) (p) W is positive
(B)
P
T
A
B
(q) U is negative
(C) (r) W is negative
(D) (s) U is positive
States A and B are very close
(t) heat rejected Q < 0

24. A copper rod (initially at room temperature 20°C) of non-uniform cross section is placed between a
steam chamber at 100°C and ice-water chamber at 0°C.
Column  Column 
(A) Initially rate of heat flow 





dt
dQ
will be (p) maximum at section A
(B) At steady state rate of heat flow 





dt
dQ
will be (q) maximum at section B
(C) At steady state temperature gradient 





dx
dT
will be (r) minimum at section C
(D) At steady state rate of change of (s) minimum at section B
temperature 





dt
dT
at a certain point will be
(t) same for all section

Answers
1. (C) 2. (B) 3. (B) 4. (A) 5. (C)
6. (B) 7. (D) 8. (D) 9. (A)(B)(D) 10. (A)(C)(D)
11. (A)(C) 12. (B)(C) 13. (A) 14. (A) 15. (A)
16. (A) 17. (A) 18. (C) 19. (B) 20. (A)
21. (D) 22. (B) 23. (A) r,s,t (B) q,r,t ; (C) p, q, t (D) p
24. (A) p, r , (B) t (C) q , r (D) t

1. This Question Paper contains 22 questions.
2. For each question in Section I, you will be awarded 3 Marks if you give the correct answer and zero
3. For each question in Section II, you will be awarded 4 Marks if you give the correct answer. There is
4. For each question in Section III, you will be awarded 3 Marks if you give the correct answer and zero
5. For each question in Section IV, you will be awarded 4 Marks if you give the correct answer and zero
6. For each question in Section V, you will be awarded 6 Marks if you give ALL the correct answer(s) or
awarded :
(i) 1 Mark for correct answer in one row.
(ii) 2 Marks for correct answer in two rows.
(iii) 4 Marks for correct answer in three rows.
7. For each question in Section VI, you will be awarded 6 Marks if you give the correct answer. There is
SECTION - I
1. 4 gms of steam at 100°C is added to 20 gms of water at 46°C in a container of negligible mass.
Assuming no heat is lost to surrounding, the mass of water in container at thermal equilibrium is.
Latent heat of vaporisation = 540 cal/gm. Specific heat of water = 1 cal/gm-°C.
(A) 18 gm (B) 20 gm
(C) 22 gm (D) 24 gm
2. A diatomic ideal gas undergoes a thermodynamic change according to
the P–V diagram shown in the figure. The total heat given to the gas is
nearly (use n2 = 0.7) :
C
2P0
P0
B
A
P
V
2V0
V0
Isothermal
(A) 2.5 P0
V0
(B) 1.4 P0
V0
(C) 3.9 P0
V0
(D) 1.1 P0
V0

3. Two rods are joined between fixed supports as shown in the figure.
Condition for no change in the lengths of individual rods with the
increase of temperature will be (1
, 2
= linear expansion co-
efficient
A1
, A2
= Area of rods Y1
, Y2
= Young modulus )
1 1 1
,A ,Y 2 2 2
,A ,Y
L1 L2
(A)
2
1
A
A
=
2
2
1
1
Y
Y


(B)
2
1
A
A
=
2
2
2
1
1
1
Y
L
Y
L


(C)
2
1
A
A
=
1
1
1
2
2
2
Y
L
Y
L


(D)
2
1
A
A
=
1
1
2
2
Y
Y


4. For a gas sample with N0 number of molecules, function N(V) is given by : N(V) = 2
3
0
0
V
V
N
3
dV
dN








 for 0
 V  V0 and N(V) = 0 for V > V0. Where dN is number of molecules in speed range V to V+ dV. The rms
speed of the molecules is :
(A) 0
V
5
2
(B) 0
V
5
3
(C) 0
V
2 (D) 0
V
3
5. The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula
 = a T, where a is a positive constant and T in ºC. If the length of the rod is  at temperature 0 ºC, then
the temperature at which the length will be 2  is:
(A)
n 2

(B)
a
4
n

(C)
1

(D)
2

6. A black body emits radiation at the rate P when its temperature is T. At this temperature the wavelength
at which the radiation has maximum intensity is 0
. If at another temperature T the power radiated is
P and wavelength at maximum intensity is
2
0

then
(A) T = 2T (B) T = T/2 (C) T = T/4 (D) T = 4 T
7. Thermal coefficient of volume expansion at constant pressure for an ideal gas sample of n moles having
pressure P0
, volume V0
and temperature T0
is
(A)
0
0V
P
R
(B)
R
V
P 0
0
(C)
0
T
1
(D)
0
T
n
1
8. There are two thin spheres A and B of the same material and same thickness. They emit like black
bodies. Radius of A is double that of B. A and B have same temperature T. When A and B are
kept in a room of temperature T0 (< T), the ratio of their rates of cooling (rate of fall of temperature)
is: [ assume negligible heat exchange between A and B ]
(A) 2 : 1 (B) 1 : 1
(C) 4 : 1 (D) 8 : 1

SECTION - II
Multiple Correct Answers Type
This section contains 4 Multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out
of which ONE OR MORE may be correct.
9. During an experiment, an ideal gas is found to obzey a condition

2
P
= constant [ = density of the gas]. The
gas is initially at temperature T, pressure P and density . The gas expands such that density changes to
2

(A) The pressure of the gas changes to 2 P.
.
(B) The temperature of the gas changes to 2 T.
.
(C) The graph of the above process on the P-T diagram is parabola.
(D) The graph of the above process on the P-T diagram is hyperbola.
10. When the temperature of a copper coin is raised by 80 o
C, its diameter increases by 0.2%,
(A) percentage rise in the area of a face is 0.4%
(B) percentage rise in the thickness is 0.4%
(C) percentage rise in the volume is 0.6%
(D) coefficient of linear expansion of copper is 0.25x10-4
/ o
C.
11. Graph shows a hypothetical speed distribution for a sample of N gas
particles (for V > V0;
dV
dN
= 0)
a
V0
speed V
dN
dV
(A) The value of aV0 is 2N.
(B) The ratio Vavg/V0 is equal to 2/3.
(C) The ratio Vrms/V0 is equal to 1/ 2 .
(D) Three fourth of the total particle has a speed between 0.5 V0 and V0.
12. Pick the correct statement(s) :
(A) The rms translational speed for all ideal-gas molecules at the same temperature is not the same
but it depends on the mass.
(B) Each particle in a gas has average translational kinetic energy and the equation
2
1
mv2
rms =
2
3
kT
establishes the relationship between the average translational kinetic energy per particle and temperature
of an ideal gas. It can be concluded that single particle has a temperature.
(C) Temperature of an ideal gas is doubled from 100°C to 200°C. The average kinetic energy of each
particle is also doubled.
(D) It is possible for both the pressure and volume of a monoatomic ideal gas to change simultaneously
without causing the internal energy of the gas to change.

SECTION - III
Reasoning Type
This section contains 2 Reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out
of which ONLY ONE is correct.
13. STATEMENT–1 : A gas is kept in an insulated cylinder with a movable piston, in compressed state. As
the piston is released, temperature of the gas decreases.
STATEMENT–2 : According to the kinetic theory of gas, a molecule colliding with the piston must
rebound with less speed than it had before the collision. Hence average speed of the molecules is
reduced.
(A) Statement-1 isTrue, Statement-2 isTrue; Statement-2 is a correct explanation for Statement-1
14. Statement-1 : As the temperature of the blackbody increases, the wavelength at which the spectral
intensity (E
) is maximum decreases.
Statement-2 : The wavelength at which the spectral intensity will be maximum for a black body is
proportional to the fourth power of its absolute temperature.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
SECTION - IV
Comprehension Type
This section contains 1 Paragraphs. Based upon each paragraph, 3 Multiple choice questions have to be
answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
Comprehension (For Q. no. 15 to 17)
The atmospheric lapse rate
For small volumes of gas, according to KINETIC THEORY OF GASES, all parts of the gas are at the
same temperature. But for huge volumes of gas like atmosphere, assumption of a uniform temperature
throughout the gas is not valid. Different parts of the atmosphere are at different temperatures. Apart
from the surface of the earth, variations also occur in temperature at different heights in the atmosphere.
The decrease in temperature with height called the ATMOSPHERIC LAPSE RATE is similar at various
locations across the surface of the Earth. By analyzing the data collected at various locations, it is
found that average global lapse rate is – 6.7 °C/Km.
The linear decrease with temperature only occurs in the lower part of the atmosphere called the
TROPOSPHERE. This is the part of the atmosphere in which weather occurs and our planes fly. Above
the troposphere is the stratosphere, with an imaginary boundary separating the two layers. In the
stratosphere, temperature tends to be relatively constant.
Absorption of sunlight at the Earth’s surface warms the troposphere from below, so vertical convection
currents are continually mixing in the air. As a parcel of air rises, its pressure drops and it expands.
The parcel does work on its surrounding, so that its internal energy and therefore, its temperature
drops. Assume that the vertical mixing is so rapid as to be adiabatic and the quantity
TP(1 – )/
has a uniform value through the layers of troposphere.
(M is molecular mass of the air, R is universal gas constant, g is gravitational acc., P and T are
pressure and temperature respectively at the point under consideration and y is height.)

15. If behaviour of the mixing of parcels of air is approximately assumed to be adiabatic then lapse rate
can be expressed as :
(A) dy
dp
)
1
(
T
P


 (B) dy
dp
1
P
T











(C) R
M
g
1



 (D) dy
dp
1
1
P
T










16. Mechanical equilibrium of the atmosphere requires that the pressure decreases with altitude according
to dy
dP
= – g. Assuming free fall acceleration to be uniform, then lapse rate is given by
(A) R
Mg
1
1 









 (B) R
Mg
1
1 









(C)  
R
Mg
1


 (D)
R
Mg


17. The value of theoretical lapse rate on the earth is (use g = 9.8 m/s2
; R = 8.3 J/mol-k and M = 29 g/mol)
(A) – 9.8 K/km (B) – 9.8 K/m
(C) – 6.7 K/km (D) – 3.4 K/km
SECTION - V
Matrix - Match Type
This section contains 1 questions. Each question has four statements (A, B, C and D) given in Column-I
and five statements (p,q,r, s and t) in Column-II. Any given statement in Column-I can have correct matching
with ONE OR MORE statement(s) in Column-II. The answers to these questions have to be appropriately
marked as illustrated in the following example. If the correct matches are A-p, A-r, B-p, B-s, C-r, C-s, D-q
and D-t then the answer should be written as : A  p,r ; B p, s ; C  r, s ; D  q, t.
18. The figures given below show different processes (relating pressure P and volume V) for a given amount
of an ideal gas. W is work done by the gas and Q is heat absorbed by the gas.
Column-I Column-II
(A) In Figure (i) (p) Q > 0.
(B) In Figure (ii) (q) W < 0.
(C) In Figure (iii) (r) Q < 0.
(D) In Figure (iv) (for complete cycle) (s) W > 0.
(t) U < 0.

SECTION - VI
Integer value correct Type
This section contains 4 questions. The answer to each question is a integer type.
19. Calculate the thermal conductance (reciprocal of the thermal resistance) for axial flow of a truncated cone of
length , the radius of the two ends are r1
and r2
. Assume that thermal conductivity of the material is K.
20. Consider a vertical tube open at both ends. The tube consists of two parts, each of different cross-
sections and each part having a piston which can move smoothly in respective tubes. The two pistons
are joined together by an inextensible wire. The combined mass of the two piston is 5 kg and area of
cross-section of the upper piston is 10 cm2 greater than that of the lower piston. Amount of gas
enclosed by the pistons is one mole. When the gas is heated slowly, pistons move by 50 cm. Find rise
in the temperature of the gas, in the form
R
X
K where R is universal gas constant. Use g = 10 m/s2
and outside pressure = 105 N/m2). Fill value of X in the answer sheet.
A1
A2
m2
m1
21. One mole of monoatomic ideal gas undergoes a processABC as shown
in figure. The maximum temperature of the gas during the process
ABC is in the form
R
V
P
X
. Find X.
22. One mole of an ideal gas is kept enclosed under a light piston (area=10–2
m2
) connected by a compressed
spring (spring constant 200 N/m). The volume of gas is 0.83 m3
and its temperature is 100K. The gas
is heated so that it compresses the spring further by 0.1 m. Find the work done by the gas in the
process in joules ? (Take R = 8.3 J/K-mole and suppose there is no atmosphere).

Answers
1. (C) 2. (C) 3. (D) 4. (B) 5. (B)
6. (A) 7. (C) 8. (B) 9. (B) (D) 10. (A)(C)(D)
11. (A)(B)(C)(D) 12. (A) (D) 13. (A) 14. (C) 15. (D)
16. (A) 17. (A) 18. (A) p, s (B) s, t (C) p, s (D) q, r
19.

)
r
r
(
k 2
1

20. 75 21. 8 22. 2

2-HEAT AND THERMODYNAMICS

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