2-HEAT AND THERMODYNAMICS-PART TEST - 1
PART TEST - 1 (PT-1)
TOPIC : HEAT AND THERMODYNAMICS (PHYSICS)
Duration : 1 Hour Max. Marks : 90
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.
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)
1 kg H +
2 2
1 kg He (D)
2
1 kg H +
4 2
3 kg He
4
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:
7
(A) 8
15
(C) 16
8
(B) 7
16
(D) 15
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)
(B)
(C)
(D)
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)
185
135
85 113
(A) 27
gm (B) 17
gm (C) 32 gm (D) 17 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 f illed 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) n R T
2
(C) n R T 𝑙 n 2 1
n R T
(B)
2
(D) n R T 𝑙n 2
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:
3
(A) Q (B)
5
2
Q (C)
5
2
Q (D) Q
3
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 PV = constant for a given amount of a gas is true for :
T
(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 ends A 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
3K S T0
2a
(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 :
2
(A) 2.0 (B) 4.0 (C) 3
(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 PV 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:
13R
(A) 6
19R
(B) 6
23R
(C) 6
17R
(D) 6
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) (C) 1.5 (D)
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
L
(A) 8
(B) L 4
L
(C) 6
L
(D) 5
A nswers
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)
PART TEST - 2 (PT-2)
TOPIC : HEAT AND THERMODYNAMICS (PHYSICS)
Duration : 1 Hour Max. Marks : 88
GENERAL INSTRUCTIONS
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
Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded.
5. For each question in Section IV, you will be awarded 4 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.
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
Straight Objective Type
This section contains 8 Single choice questions. Each question has choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
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 ?
9
(A) p0V0 (B) 2p0V0 (C) p0V0 𝑙n 8
(D) p0V0 𝑙n 2
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 rods of same dimensions, but made of different materials are joined end to end with their free ends being 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:
63
(A) 25
73
P0 (B) 25 P0
48
(C) 25
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 rods of metal are welded end to end in series between 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 between A 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 P
shown by pressure- density curve.
(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 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
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 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.
15. Statement-1 : Burns sustained from steam at 100oC are usually more serious than those sustained by boiling water (at 100oC)
Statement-2 : To convert 1gm of water at 100oC to 1 gm of steam at 100oC, 540 calories of heat is to be supplied. Hence 1gm of steam at 100oC has more heat content than 1 gm of water at 100oC
(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
16. Statement-1 : If the absolute temperature of a gas is doubled, the final rms-velocity of the gas particles
becomes times the initial value.
1
Statement-2: The average translational kinetic energy of molecules in a gas is equal to both
2 mv
2
rms
and
3 kT.( where v
2
rms
, k and T have usual meanings)
(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.
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 mass of the ice formed due to conversion from the water till thermal equilibrium is reached, is equal 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.
W
20. For this process, the ratio nRT
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
Q nRT1
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 C has value
R
(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 Ι Column ΙΙ
(A) (p) W is positive
(B) (q) U is negative
T
(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 Ι Column ΙΙ
dQ
(A) Initially rate of heat flow dt will be (p) maximum at section A
dQ
(B) At steady state rate of heat flow dt will be (q) maximum at section B
(C) At steady state temperature gradient
dT
dx
will be (r) minimum at section C
(D) At steady state rate of change of
(s) minimum at section B
temperature dT
at a certain point will be
dt
(t) same for all section
A nswers
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
PART TEST - 3 (PT-3)
TOPIC : HEAT AND THERMODYNAMICS (PHYSICS)
Duration : 1 Hour Max. Marks : 88
GENERAL INSTRUCTIONS
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
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
Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded.
5. For each question in Section IV, you will be awarded 4 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.
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 no negative marking.
SECTION - I
Straight Objective Type
This section contains 8 Single choice questions. Each question has choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
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
2P0
P0
nearly (use 𝑙n2 = 0.7) :
(A) 2.5 P0V0 (B) 1.4 P0V0 V
(C) 3.9 P0V0
(D) 1.1 P0V0
V0 2V0
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 ( ,
= linear expansion co-
efficient
A1, A2 = Area of rods Y1, Y2 = Young modulus )
(A) A1 A 2
1Y1
= 2 Y2
(B) A1
A 2
L11Y1
= L2 2 Y2
(C) A1
A 2
L2 2 Y2
= L11Y1
(D) A1
A 2
2 Y2
= 1Y1
dN 3N0 2
4. For a gas sample with N0 number of molecules, function N(V) is given by : N(V) =
3 V
for 0
dV V0
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) V0
(B) V0 0 0
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 𝑙 at temperature 0 ºC, then the temperature at which the length will be 2 𝑙 is:
1 2
(A)
(B)
(C)
(D)
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 . If at another temperature T the power radiated is
P and wavelength at maximum intensity is
0
2 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)
R (B) P0 V0
(C)
1 1
(D)
P0 V0
R T0
n T0
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.
P2
9. During an experiment, an ideal gas is found to obzey a condition
= 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 P.
(B) The temperature of the gas changes to 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 oC, 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 / oC.
11. Graph shows a hypothetical speed distribution for a sample of N gas
particles (for V > V ; dN = 0) a
0 dV
(A) The value of aV0
is 2N. dN
(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
12. Pick the correct statement(s) :
and V0.
V0
speed V
(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
1mv2
2
rms
= 3 kT
2
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 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.
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
(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.
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 :
P ( 1) dp
T 1 dp
(A) T dy
(B)
dy
1 gM T 1 dp
(C) R
(D) P 1 dy
16. Mechanical equilibrium of the atmosphere requires that the pressure decreases with altitude according
dP
to dy = – g. Assuming free fall acceleration to be uniform, then lapse rate is given by
1 Mg 1 Mg
(A) 1 R (B) 1 R
(C) 1Mg
R
(D) Mg
R
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 𝑙, 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
X K where R is universal gas constant. Use g = 10 m/s2
R
and outside pressure = 105 N/m2). Fill value of X in the answer sheet.
m1
21. One mole of monoatomic ideal gas undergoes a process ABC as shown in figure. The maximum temperature of the gas during the process
ABC is in the form
XP V . Find X.
R
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).
A nswers
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.
k(r1 r2 )
𝑙
20. 75 21. 8 22. 2
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