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Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

TEST CODE : GST [1]

ROLL NO.

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Three perfect gases at absolute temperatures T1, T2 and T3 are mixed. The masses of molecules are m1, m2 and m3 and the number of molecules are n1, n2 and n3 respectively. Assuming no loss of energy, the final temperature of the mixture is : (A)

n1 T1 n2T2 n3T3 n1 n2 n3

(B)

n1 T12 n2T22 n3T33 n1T1 n2T2 n3T3

(C)

n12T12 n22T22 n32 T32 n1T1 n2T2 n3T3

(D)

T1 T2 T3 3

2.

Two balloon are filled, one with pure He gas and the other by air, respectively. If the pressure and temperature of these balloons are same, then the number of molecules per unit volume is : (A) more in the He filled balloon (B) same in both balloon (C) more in air filled balloon (D) in the ratio of 1 4

3.

The mean kinetic energy of one mole of gas per degree of freedom (on the basis of kinetic theory of gases) is: (A)

4.

1 kT 2

(B)

3 kT 2

6.

(C)

The temperature of the system decreases in the process of : (A) free expansion (B) (C) isothermal expansion (D)

(D)

1 RT 2

2.1 kJ

(D)

4.2 kJ

adiabatic expansion isothermal compression

CV and CP denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then : (A) C p CV is larger for a diatomic ideal gas than for a monoatomic ideal gas (B) (C) (D)

7.

3 RT 2

100 g of water is heated from 30C to 50C . Ignoring the slight expansion of the water, the change in its internal energy is : (Specific heat of water is 4184 J/kg/K) (A) 8.4 kJ (B) 84 kJ

5.

(C)

C p CV is larger for a diatomic ideal gas than for a monoatomic ideal gas

Cp Cr

is larger for a diatomic ideal gas than for a monoatomic ideal gas

C p . CV is larger for a diatomic ideal gas than for a monoatomic ideal gas

The temperature of the system decreases in the process of (A) free expansion (B) (C) isothermal expansion (D)

VMC/Gasesous State & Thermodynamics

77

adiabatic expansion isothermal compression

HWT/Physics

Vidyamandir Classes 8.

In an adiabatic process where pressure is increased by (A)

9.

4 % 9

(B)

2 % 3

Cp 3 2 % if , then the volume decreases by about. 3 CV 2 (C)

4%

(D)

9 % 4

In a Carnot engine, the temperature of reservoir is 927C and that of sink is 27C . If the work done by the engine when it transfer heat form reservoir to sink is 12.6 106 J , the quantity of heat absorbed by the engine from the reservoir is: (A)

10.

16.8 106 J

(B)

4 106 J

(C)

7.6 106 J

(D)

4.25 106 J

A bubble of 8 mole of helium is submerged at a certain depth in water. The temperature of water increases by 30C How much heat is added approximately to helium during expansion? (A) 400-0 J (B) 30000 J (C) 3500 J (D) 4500 J

VMC/Gasesous State & Thermodynamics

78

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : GST [2]

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked with ‘*’ may have More than One correct option. 1.

A container with insulating walls is divided into two equal parts by a partition fitted with a valve. One part is filled with an ideal gas at a pressure p and temperature T, whereas the other part is completely evacuated. If the valve is suddenly opened, the pressure and temperature of the gas will be : p p T T T T ? p p (A) (B) (C) (D) 2 2 2 2 2

2.

The tyre of a motor car contains air at 15C . If the temperature increases to 35C , the approximate percentage increase in pressure is : (ignore to expansion of tyre) (A) 7 (B) 9 (C) 11 (D) 13

3.

The gases carbon – monoxide (CO) and nitrogen at the same temperature have kinetic energies E1 and E2 respectively. Then: (A) (B) (C) (D) E1 and E2 cannot be compared E1 E 2 E1 E2 E1 E2

4.

The figure shows the p V plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semi-circule and CDA is half of an ellipse. Then : (A) the process during the path A A B is isothermal (B)

heat flows out of the gas during the path B C D

(C)

work done during the path A B C is zero

(D)

positive work is done by the gas in the cycle ABCDA

5.

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature T0, while box B contains one mole of helium at temperature (7/3)T0. The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (Ignore the heat capacity of boxes). Then, the final temperature of the gases Tf, in terms of T0 is : 3 7 3 5 T f T0 T f T0 T f T0 T f T0 (A) (B) (C) (D) 7 3 2 2

6.

The change in internal energy of a given mass of gas, when its volume changes from V to 2V at constant pressure p is : (

Cp CV

(A)

, universal gas constant = R)

pV

(B)

pV 1

2

VMC/Gasesous State & Thermodynamics

(C)

79

pV 2 1

(D)

pV 1

HWT/Physics

Vidyamandir Classes 7.

A gas is suddenly expanded such that its final volume becomes 3 times its initial volume. If the specific heat at constant volume of the gas is 2R, then the ratio of initial to final pressure is nearly equal to : (A) 5 (B) 6.5 (C) 7 (D) 3.5

8.

An ideal monoatomic gas at 27C is compressed adiabatically to 8/27 times of its present volume. The increase in temperature of the gas is: (A) 375C (B) 402C (C) 175C (D) 475C

9.

An ideal refrigerator has a freezer at a temperature of 13C . The coefficient of performance of the engine in 5. The temperature of the air (to which heat is rejected) will be : (A) 127C (B) 325 K (C) 39³C (D) 320C

10.

Two moles of oxygen is mixed with eight moles of helium. The effective specific heat of the mixture at constant volume is: (A) 1.3R (B) 1.4 R (C) 1.7 R (D) 1.7 R

VMC/Gasesous State & Thermodynamics

80

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : GST [3]

ROLL NO.

START TIME :

END TIME :

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked with ‘*’ may have More than One correct option. 1.

2.

A real gas behaves like an ideal gas if its : (A) pressure and temperature are both high (C) pressure is high and temperature is low

(B) (D)

pressure and temperature are both low pressure is low and temperature is high

A horizontal uniform glass tube of 100 cm length sealed at both ends contains 10cm mercury column in the middle. The temperature and pressure are same of air on either side of mercury. If the air column at one end is kept at 0C and the other end at 273C , the pressure of air which is at 0C is (in cm of Hg) (A) 76 (B) 88.2 (C)

102.4

(D)

12.2

3.

It is seen that in proper ventilation of building, windows must be opened near the bottom and the top of the walls, so as to let pass: (A) In hot near the roof and cool air out near the bottom (B) out hot air near the roof (C) in cool air near the bottom and hot air out near the roof (D) in more air

4.

One mole of an ideal gas having initial volume V, pressure 2p and temperature T undergoes a cyclic process ABCDA as shown. The net work done in the complete cycle is :

5.

6.

(A)

zero

(B)

1 RT n 2 2

(C)

RT n 2

(D)

3 RT n 2 2

An ideal gas is taken from point A to the point B, as shown in the p-V diagram, keeping the temperature constant. The work done in the process is : (A)

p A pB VB VA

(B)

1 pB p A VB VA 2

(C)

1 pB p A VB VA 2

(D)

1 p A pB VB VA 2

An ideal gas is allowed to expand freely against a vacuum in a rigid insulated container. The gas undergoes. (A) an increase in its internal energy (B) a decrease in its internal energy (C) neither an increase nor a decrease in its temperature or internal energy (D) a decrease in temperature

VMC/Gasesous State & Thermodynamics

81

HWT/Physics

Vidyamandir Classes 7.

During the adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio CP / CV for the gas is : (A)

8.

9.

(B)

2

(C)

5/3

(D)

3/2

7 The pressure and density of a given mass of a diatomic gas change adiabatically from (p, d) to 5 p then is 9 = ratio of specific heats) p (A) 1/128 (B) 1/64 (C) 64 (D) 128

p d . If

d 32 , d

What is the value of sink temperature when efficiency of engine is 100% ?

(A) 10.

4/3

zero

(B)

300 K

(C)

273 K

(D)

400 K

One mole of monoatomic gas and three moles of diatomic gas are put together in a container. The molar specific heat (in J K 1 mol 1 ) (A)

18.7

(B)

18.9

VMC/Gasesous State & Thermodynamics

(C)

82

19.2

(D)

None of these

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

TEST CODE : GST [4]

ROLL NO.

START TIME :

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

1 mol of gas occupies a volume of 200 mL at 100 mm pressure. What is the volume occupied by two moles of gas at 400 mm pressure and at same temperature? (A) 50 mL (B) 100 mL (C) 200 mL (D) 400 mL

2.

The molecules of a given mass of a gas have a rms velocity of 200 m/s at 27C and 1.0 105 N / m 2 pressure. When the temperature is 127C and pressure is 0.5 105 N / m 2 , the rms velocity in m/s will be : (A)

3.

100 2

(C)

400 3

(D)

None of these\

9mA = 4mB

(B)

3mA = 2mB

(C)

2mA = 3mB

(D)

4mA = 9mB

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V1 and contains ideal gas at pressure p1 and temperature T1. The other chamber has volume V2 and contains ideal gas at pressure p2 and temperature T2. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be : (A)

5.

(B)

Two identical vessels A and B with frictionless pistons contain the same ideal gas at the same temperature and the same volume V. The masses of gas in A B are mA and mB respectively. The gases are allowed to expand isothermally to same final volume 2 V. The change in pressure of the gas in A and B found to be Δp and 1.5 p respectively. Then: (A)

4.

100 2 3

T1T2 p1V1 p2V2 p1V1T2 p2V2T1

(B)

p1V1T1 p2V2T2 p1V1 p2V2

(C)

p1V1T2 p2V2T1 p1V1 p2V2

(D)

T1T2 p1V1 p2V2 p1V1T1 p2V2T2

The ratio of specific heats of a gas is . The change in internal energy of one mole of the gas, when the volume changes from V to 2V at constant pressure p is: (A)

1 pV

(B)

pV

(C)

pV 1

(D)

pV

6.

In the adiabatic compression, the decrease in volume is associated with (A) increase in temperature and decrease in pressure (B) decrease in temperature and increase in pressure (C) decrease in temperature and decrease in pressure (D) increase in temperature and increase in pressure

7.

An ideal gas expands isothermally. Initial pressure is p1 and final pressure is p3.The total work done is W. Then (A) (B) (C) (D) p3 p1 W 0 p3 p1 W 0 p3 p1 W 0 p3 p1 W 0

8.

Cp 1.4 Adiabatic modulus of elasticity of a gas is 2.1 105 Nm 2 . What will be its isothermal modulus of elasticity ? C V

(A)

1.2 105 Nm 2

(B)

4 105 Nm 2

VMC/Gasesous State & Thermodynamics

(C)

83

1.5 105 Nm 2

(D)

1.8 105 Nm 2

HWT/Physics

Vidyamandir Classes 9.

10.

When water is converted into ice, its entropy : (A) increases (C) remains unchanged

(B) (D)

decreases first decreases and then increases

70 cal of heat is required to raise the temperature of 2 moles of an ideal gas from 30C to 35C while the pressure of the gas is kept constant. The amount of the heat required to raise the temperature of the same gas through the same temperature range at constant volume is (gas constant R = 2cal mol 1 K 1 ) (A)

70 cal

(B)

60 cal

VMC/Gasesous State & Thermodynamics

(C)

84

50 cal

(D)

30 cal

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

TEST CODE : GST [5]

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

If universal gas constant is R, the essential heat to increase temperature from 273 K to 473 K at constant volume for ideal gas of 4 mol is : (A) 200 R (B) 400 R (C) 800 R (D) 1200 R

2.

An ideal gas ( 1.5 ) is expanded adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of molecules 2.0 times? (A) 4 times (B)

16 times

(C)

8 times

(D)

2 times

3.

If masses of all molecules of a gas are halved and their speeds are doubled, then the ratio of initial and final pressure : (A) 1:2 (B) 2:1 (C) 4:1 (D) 1:4

4.

When a system is taken from state i to state f along the path iaf, it is found that Q = 50 cal and W = 20 cal. Along the path ibf, Q = 36 cal. W along the path ibf is :

5.

(A)

6 cal

(B)

16 cal

(C)

66 cal

(D)

14 cal

A perfect gas goes from state A to another state B by absorbing 8 105 J of heat and doing 6.5 105 J of external work. It is now transferred between the same two states in another process in which it absorbs 105 J of heat in the second process. Then :

6.

(A)

work done on the gas is 0.5 105 J

(B)

work done by gas is 0.5 105 J

(C)

work done on gas is 105 J

(D)

work done by gas is 105 J

1 mm3 of gas is compressed at 1 atm pressure and temperature 27C to 627C . What is the final pressure under adiabatic condition? ( for the gas = 1.5) (A)

7.

27 105 Nm 2

(B)

12 105 Nm 2

(C)

15 105 Nm 2

(D)

23 103 Nm 2

Unit mass of a liquid volume V1 is completely charged into a gas of volume V2 at a constant external pressure p and temperature T. If the latent heat of evaporation for the given mass is L, then the increase in the internal energy of the system is: (A)

8.

zero

(B)

p V2 V1

(C)

L p V2 V1

A Carnot engine operating between temperature T1 and T2 has efficiency 1 . Then T1 and T2 are respectively. 3 (A) 372 K and 330 K (B)

330 K and 268 K

VMC/Gasesous State & Thermodynamics

(C)

85

(D)

L

1 . When T2 is lowered by 62 K, its efficiency increase to 6

310 K and 248 K

(D)

372 K and 310 K

HWT/Physics

Vidyamandir Classes 9.

When you make ice cubes, the entropy of watre (A) does not change (B) increases (C) decreases (D) may either increase or decrease depending on the process used

10.

The temperature of 5 moles of a gas at constant volume is changed from 100C to 120C . The change in internal energy 80J. The total heat capacity of the gas at constant volume will be in JK 1 is: (A) 8 (B) 4 (C) 0.8

VMC/Gasesous State & Thermodynamics

86

(D)

0.4

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

TEST CODE : GST [6]

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

An ideal gas is expanding such that pT2 = constant. The coefficient of volume expansion of the gas is : 1 2 3 4 (A) (B) (C) (D) T T T T The rms velocity of gas molecules is 300ms 1 . The rms velocity of molecules of gas with twice the molecular weight and half the absolute temperature is : (A)

300 ms 1

(B)

600 ms 1

(C)

75ms 1

(D)

150 ms 1

3.

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

4.

A thermodynamical system is changed from state (p1, V1) to (p2, V2) by two different process, quantity which will remain same will be : ΔQ (A) (B) ΔW (C) (D) ΔQ ΔW ΔQ ΔW

5.

The p–V diagram of a system undergoing thermodynamic transformation is shown in figure. The work done by the system in going from A B C is 30 J, and 40 J heat is given to the system. The change in internal energy between A and C is: (A) 10 J (B) 70 J (C) 84 J (D) 134 J

6.

A monoatomic gas is suddenly compressed to (1/8)th of its initial volume. The ratio of its final pressure to the initial pressure is (Given the ratio of the specific heats of the given gas to be 5/3) (A) 32 (B) 40/3 (C) 24/8 (D) 8

7.

A given mass of a gas is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restored and is pressure is then found to be 0.75 of its initial pressure. The ratio of the specific heats of the gas is approximately. (A) 1.20 (B) 1.41 (C) 1.67 (D) 1.83

8.

A Carnot engine whose efficiency is 40% , receives heat at 500 K. If the efficiency is to be 50% , the source temperature for the same exhaust temperature is: (A) 900 K (B) 600 K (C) 700 K (D) 800 K

9.

An ideal heat engine exhausting at 27C is to have 25% efficiency. It must take heat at (A)

10.

127C

(B)

227C

(C)

327C

(D)

None of these

At what temperature the rms velocity of helium molecules will be equal to that of hydrogen molecules at NTP? (A) 844 K (B) 64 K (C) 273C (D) 273 K

VMC/Gasesous State & Thermodynamics

87

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

TEST CODE : GST [7]

ROLL NO.

START TIME :

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked with ‘*’ may have More than One correct option. 1.

One litre of oxygen at a pressure of 1 atm and two litres of nitrogen at a pressure of 0.5 atm, are introduced into a vessel of volume 1L. If there is no change in temperature, the final pressure of the mixture of gas (in atm) is: (A) 1.5 (B) 2.5 (C) 2 (D) 4

2.

The ratio of the vapour densities of two gases at a given temperature is 9 : 8. The ratio of the rms velocities of their molecules is: (A)

3.

32 2

(B)

2 2 3

(C)

9:8

`

(D)

8:9

The temperature of a gas is 68C . At what temperature will the average kinetic energy of its molecules be twice that of at

68C ? (A)

130C

(B)

127C

(C)

100C

(D)

105C

4.

310 J of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 25C to 35C . The amount of heat required to rise the temperature of the gas through the same range at constant volume is : (A) 384 J (B) 144 J (C) 276 J (D) 425 J

5.

A sample of ideal monoatomic gas is taken round the cycle ABCA as shown in the figure. The work done during the cycle is :

6.

(A)

3 pV

(B)

zero

(C)

9 pV

(D)

6pV

Ideal gas undergoes an adiabatic change in its state from (p1, V1, T1) to (p2, V2, T2). The work done (W) in the process is ( = number of molecules, Cp, and CV are molar specific heats of gas)

7.

(A)

W C p T1 T2

(B)

W CV T1 T2

(C)

W CP T1 T2

(D)

W CV T1 T2

7 The pressure and density of a diatomic gas change adiabatically from 5

should be: (A) 16 8.

(B)

32

(C)

64

p1 1

to

(D)

p2 2 . If

2 p 32 , then 2 1 p1

128

A diatomic ideal gas is used in a car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from V to 32V. The efficiency of the engine is: (A) 0.5 (B) 0.75 (C) 0.99 (D) 0.25

VMC/Gasesous State & Thermodynamics

88

HWT/Physics

Vidyamandir Classes 9.

The sink temperature of a heat engine 77C . The efficiency is 30% . The source temperature is: (A)

10.

500C

(B)

227C

(C)

317C

(D)

427C

Four molecules of a gas have speeds 1, 2, 3 and 4kms 1 . The value of rms speed of the gas molecules is ; (A)

1 15 kms 1 2

(B)

1 10 kms 1 2

VMC/Gasesous State & Thermodynamics

(C)

89

25kms 1

(D)

15 kms 1 2

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

TEST CODE : GST [8]

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Volume-temperature graph at atmospheric pressure for a monoatomic gas (V in m3, T in C ) is:

(A)

2.

(B)

(C)

(D)

If the rms velocity of a gas is v, then : (A)

v 2T = constant

(B)

v 2 / T constant (C)

vT2 = constant

(D)

v is independent of T

3.

One mole of a monatomic ideal gas is mixed with one mole of a diatomic ideal gas. The molar specific heat of the mixture at constant volume is: (A) (3/2) R (B) (5 / 2) R (C) 2R (D) 4R

4.

Two cylinder A and B fitted with pistons, contain equal number of moles of an ideal monoatomic gas at 400 K. The piston of A is free to move while that of B is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in A is 42 K, the rise in temperature of the gas in B is ( 5 / 3 ) (A)

25.2 K

(B)

35 K

(C)

42 K

(D)

70 K

5.

5.6 of helium gas at STP is adiabatically compressed to 0.7 L. Taking the initial temperature of be T1, the work done in the process is : 9 3 15 9 RT1 RT1 RT1 RT1 (A) (B) (C) (D) 8 2 8 2

6.

The work of 146 kJ is performed in order to compress one kilo mole of a gas adiabatically and in this process the temperature of the gas increases by 7C . The gas is ( R 8.3J mol 1K 1 ) (A) (C)

7.

diatomic a mixture of monotomic and diatomic

(B) (D)

triatomic monoatomic

Ten moles of an ideal gas at constant temperature 500 K is compressed from 50 L to 5 L. Work done in the process is (Given, R = 8.31 J mol 1K 1 ) (A)

8.

1.2 104 J

(B)

2.4 104 J

(C)

4.8 104 J

(D)

9.6 104 J

The efficiency of Carnot’s heat engine is 0.5, when the temperature of the source is T1 and that of sink is T2. The efficiency of another Carnot’s heat engine is also 0.5. The temperature of source and sink of the second engine are respectively. T 2T1 2 (A) (B) (C) (D) 2T1 2T2 T1 5 T2 5 T1 10T2 10 2

VMC/Gasesous State & Thermodynamics

90

HWT/Physics

Vidyamandir Classes 9.

A Carnot engine takes heat from a reservoir at 627C and rejects heat to a sink at 27C . Its efficiency will be : (A) 3/5 (B) 1/3 (C) 2/3 (D) 200/209

10.

To what temperature should the hydrogen at 327C be cooled at constant pressure, so that the root mean square velocity of its molecules becomes half of its previous value? (A) 123C (B) 123C (C) 100C (D) 0C

VMC/Gasesous State & Thermodynamics

91

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : GST [9]

ROLL NO.

START TIME :

END TIME :

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A bubble is at the bottom of the lake of depth h. As the bubble comes to sea level, its radius increases three times. If atmospheric pressure is equal to l meter of water column, then h is equal to : (A) 26l (B) l (C) 25l (D) 30l

2.

KE per unit volume is E. The pressure exerted by the gas is given by : E 2E 3E (A) (B) (C) 3 3 2

3.

5.

E 2

5 7 If one mole of a monoatomic gas is mixed with one mole of a diatomic gas , the value of for the mixture is : 3 5

(A) 4.

(D)

1.40

(B)

1.50

(C)

1.53

(D)

3.07

An ideal gas expands along the path AB as shown in the p-V diagram. The work done is : (A)

4 104 J

(B)

1.2 105 J

(C) (D)

2.4 105 J None of the above

An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume : ( 1, 4 and 21.4 0.38 ). The ratio of the final to initial pressure is : (A)

0.76 : 1

(B)

1:1

(C)

0.66 : 1

(D)

0.86 : 1

6.

During an adiabatic process, the cube of the pressure is found to be inversely proportional to the fourth power of the volume. Then the ratio of specific heat is : (A) 1 (B) 1.33 (C) 1.67 (D) 1.4

7.

During an isothermal expansion of an ideal gas : (A) its internal energy decreases (B) its internal energy does not change (C) The work done by the gas is equal to the quantity of heat absorbed by it : (D) Both (B) and (C) are correct

8.

Three designs are proposed for an engine operating between 500 K and 300 K. For 1 kcal of heat input, design A claims to produce 3000 J of work, design B claims to produce 2000 J of work and design C claims to produce 1680 J of work. The design which is possible (A) A only (B) B only (C) C only (D) All of these

VMC/Gasesous State & Thermodynamics

92

HWT/Physics

Vidyamandir Classes 9.

A Carnot engine, having an efficiency of 1 / 10 as heat engine, is used as a refrigerator. If the work done on the system 10 J, the amount energy absorbed from the reservoir at lower temperature is : (A) 99 J (B) 90 J (C) 1J

10.

(D)

100 J

In a Carnot engine, when T2 0C and T1 200C , its efficiency is 1 and when T1 0C T2 200C , its efficiency is 2 , then what is 1 / 2 , then what is 1 / 2 ? (A)

0.577

(B)

0.733

VMC/Gasesous State & Thermodynamics

(C)

93

0.638

(D)

Cannot be calculated

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

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ROLL NO.

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

Two gases A and B having same pressure p, volume V and absolute temperature T are mixed. If the mixture has the volume and temperature as V and T respectively, then the pressure of the mixture is: (A) 2p (B) p (C) p/2 (D) 4p One kg of a diatomic gas is at a pressure of 8 104 Nm 2 . The density of the gas is 4kgm 3 . What is the energy of the gas due to its thermal motion? (A)

3.

(B)

6 104 J

(D)

7 104 J

R (B) (C) (D) CV R CV 2 R CV 3R 2 1 cm3 of water at its boiling point absorbs 540 cal of heat of become steam with a volume of 1671 cm3. If the atmospheric

Nm 2 and the mechanical equivalent of heat = 419 J cal 1 , the energy spent in this process in

overcoming intermolecular force is : (A) 540 cal (B)

6.

(C)

CV

pressure = 1.013 105

5.

5 104 J

For a gas molecule with 6 degrees of freedom the law of equipartition of energy gives the following relation between the molecular specific heat (CV) and gas constant (R) : (A)

4.

3 104 J

40 cal

(C)

500 cal

(D)

zero

One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is p0. Choose the correct option (s) from the following : (A) Internal energies at A and B are the same (B) Work done by the gas in process AB in p0V0 In 4 p0 4

(C)

Pressure at C is

(D)

T Temperature at C is 0 4

One mole of an ideal gas at an initial temperature of T Kelvin does 6R joule of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is 5/3, the final temperature of gas will be : (A)

(T + 2.4) K

(B)

T 2 .4 K

(C)

T 4 K

(D)

T 4 K

7.

A container having 1 mole of a gas at a temperature 27C has a movable piston which maintains at constant pressure in container of 1 atm. The gas is compressed until temperature becomes 127°C. The work done is (Cp for gas is 7.03 cal/mol – K) (A) 703 J (B) 814 J (C) 121 J (D) 2035 J

8.

A Carnot engine working between 450 K and 600 K has a work output of 300 J/cycle. The amount of heat energy supplied to the engine from the source in each cycle is : (A) 400 J (B) 800 J (C) 1600 J (D) 1200 J

VMC/Gasesous State & Thermodynamics

94

HWT/Physics

Vidyamandir Classes 9.

A Carnot’s engine operates with source at 127C and sink at 27C . If the source supplies 40 kJ of heat energy, the work done by the engine is : (A) 30 kJ (B) 10 kJ (C) 4 kJ (D) 1 kJ

10.

A Carnot engine takes 3 106 cal of heat form a reservoir at 627C and gives it to a sink at 27C . The work done by the engine is : (A)

4.2 106 J

(B)

8.4 106

VMC/Gasesous State & Thermodynamics

(C)

95

1.68 106 J

(D)

zero

HWT/Physics

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Three perfect gases at absolute temperatures T1, T2 and T3 are mixed. The masses of molecules are m1, m2 and m3 and the number of molecules are n1, n2 and n3 respectively. Assuming no loss of energy, the final temperature of the mixture is : (A)

n1 T1 n2T2 n3T3 n1 n2 n3

(B)

n1 T12 n2T22 n3T33 n1T1 n2T2 n3T3

(C)

n12T12 n22T22 n32 T32 n1T1 n2T2 n3T3

(D)

T1 T2 T3 3

2.

Two balloon are filled, one with pure He gas and the other by air, respectively. If the pressure and temperature of these balloons are same, then the number of molecules per unit volume is : (A) more in the He filled balloon (B) same in both balloon (C) more in air filled balloon (D) in the ratio of 1 4

3.

The mean kinetic energy of one mole of gas per degree of freedom (on the basis of kinetic theory of gases) is: (A)

4.

1 kT 2

(B)

3 kT 2

6.

(C)

The temperature of the system decreases in the process of : (A) free expansion (B) (C) isothermal expansion (D)

(D)

1 RT 2

2.1 kJ

(D)

4.2 kJ

adiabatic expansion isothermal compression

CV and CP denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then : (A) C p CV is larger for a diatomic ideal gas than for a monoatomic ideal gas (B) (C) (D)

7.

3 RT 2

100 g of water is heated from 30C to 50C . Ignoring the slight expansion of the water, the change in its internal energy is : (Specific heat of water is 4184 J/kg/K) (A) 8.4 kJ (B) 84 kJ

5.

(C)

C p CV is larger for a diatomic ideal gas than for a monoatomic ideal gas

Cp Cr

is larger for a diatomic ideal gas than for a monoatomic ideal gas

C p . CV is larger for a diatomic ideal gas than for a monoatomic ideal gas

The temperature of the system decreases in the process of (A) free expansion (B) (C) isothermal expansion (D)

VMC/Gasesous State & Thermodynamics

77

adiabatic expansion isothermal compression

HWT/Physics

Vidyamandir Classes 8.

In an adiabatic process where pressure is increased by (A)

9.

4 % 9

(B)

2 % 3

Cp 3 2 % if , then the volume decreases by about. 3 CV 2 (C)

4%

(D)

9 % 4

In a Carnot engine, the temperature of reservoir is 927C and that of sink is 27C . If the work done by the engine when it transfer heat form reservoir to sink is 12.6 106 J , the quantity of heat absorbed by the engine from the reservoir is: (A)

10.

16.8 106 J

(B)

4 106 J

(C)

7.6 106 J

(D)

4.25 106 J

A bubble of 8 mole of helium is submerged at a certain depth in water. The temperature of water increases by 30C How much heat is added approximately to helium during expansion? (A) 400-0 J (B) 30000 J (C) 3500 J (D) 4500 J

VMC/Gasesous State & Thermodynamics

78

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked with ‘*’ may have More than One correct option. 1.

A container with insulating walls is divided into two equal parts by a partition fitted with a valve. One part is filled with an ideal gas at a pressure p and temperature T, whereas the other part is completely evacuated. If the valve is suddenly opened, the pressure and temperature of the gas will be : p p T T T T ? p p (A) (B) (C) (D) 2 2 2 2 2

2.

The tyre of a motor car contains air at 15C . If the temperature increases to 35C , the approximate percentage increase in pressure is : (ignore to expansion of tyre) (A) 7 (B) 9 (C) 11 (D) 13

3.

The gases carbon – monoxide (CO) and nitrogen at the same temperature have kinetic energies E1 and E2 respectively. Then: (A) (B) (C) (D) E1 and E2 cannot be compared E1 E 2 E1 E2 E1 E2

4.

The figure shows the p V plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semi-circule and CDA is half of an ellipse. Then : (A) the process during the path A A B is isothermal (B)

heat flows out of the gas during the path B C D

(C)

work done during the path A B C is zero

(D)

positive work is done by the gas in the cycle ABCDA

5.

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature T0, while box B contains one mole of helium at temperature (7/3)T0. The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (Ignore the heat capacity of boxes). Then, the final temperature of the gases Tf, in terms of T0 is : 3 7 3 5 T f T0 T f T0 T f T0 T f T0 (A) (B) (C) (D) 7 3 2 2

6.

The change in internal energy of a given mass of gas, when its volume changes from V to 2V at constant pressure p is : (

Cp CV

(A)

, universal gas constant = R)

pV

(B)

pV 1

2

VMC/Gasesous State & Thermodynamics

(C)

79

pV 2 1

(D)

pV 1

HWT/Physics

Vidyamandir Classes 7.

A gas is suddenly expanded such that its final volume becomes 3 times its initial volume. If the specific heat at constant volume of the gas is 2R, then the ratio of initial to final pressure is nearly equal to : (A) 5 (B) 6.5 (C) 7 (D) 3.5

8.

An ideal monoatomic gas at 27C is compressed adiabatically to 8/27 times of its present volume. The increase in temperature of the gas is: (A) 375C (B) 402C (C) 175C (D) 475C

9.

An ideal refrigerator has a freezer at a temperature of 13C . The coefficient of performance of the engine in 5. The temperature of the air (to which heat is rejected) will be : (A) 127C (B) 325 K (C) 39³C (D) 320C

10.

Two moles of oxygen is mixed with eight moles of helium. The effective specific heat of the mixture at constant volume is: (A) 1.3R (B) 1.4 R (C) 1.7 R (D) 1.7 R

VMC/Gasesous State & Thermodynamics

80

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

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ROLL NO.

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked with ‘*’ may have More than One correct option. 1.

2.

A real gas behaves like an ideal gas if its : (A) pressure and temperature are both high (C) pressure is high and temperature is low

(B) (D)

pressure and temperature are both low pressure is low and temperature is high

A horizontal uniform glass tube of 100 cm length sealed at both ends contains 10cm mercury column in the middle. The temperature and pressure are same of air on either side of mercury. If the air column at one end is kept at 0C and the other end at 273C , the pressure of air which is at 0C is (in cm of Hg) (A) 76 (B) 88.2 (C)

102.4

(D)

12.2

3.

It is seen that in proper ventilation of building, windows must be opened near the bottom and the top of the walls, so as to let pass: (A) In hot near the roof and cool air out near the bottom (B) out hot air near the roof (C) in cool air near the bottom and hot air out near the roof (D) in more air

4.

One mole of an ideal gas having initial volume V, pressure 2p and temperature T undergoes a cyclic process ABCDA as shown. The net work done in the complete cycle is :

5.

6.

(A)

zero

(B)

1 RT n 2 2

(C)

RT n 2

(D)

3 RT n 2 2

An ideal gas is taken from point A to the point B, as shown in the p-V diagram, keeping the temperature constant. The work done in the process is : (A)

p A pB VB VA

(B)

1 pB p A VB VA 2

(C)

1 pB p A VB VA 2

(D)

1 p A pB VB VA 2

An ideal gas is allowed to expand freely against a vacuum in a rigid insulated container. The gas undergoes. (A) an increase in its internal energy (B) a decrease in its internal energy (C) neither an increase nor a decrease in its temperature or internal energy (D) a decrease in temperature

VMC/Gasesous State & Thermodynamics

81

HWT/Physics

Vidyamandir Classes 7.

During the adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio CP / CV for the gas is : (A)

8.

9.

(B)

2

(C)

5/3

(D)

3/2

7 The pressure and density of a given mass of a diatomic gas change adiabatically from (p, d) to 5 p then is 9 = ratio of specific heats) p (A) 1/128 (B) 1/64 (C) 64 (D) 128

p d . If

d 32 , d

What is the value of sink temperature when efficiency of engine is 100% ?

(A) 10.

4/3

zero

(B)

300 K

(C)

273 K

(D)

400 K

One mole of monoatomic gas and three moles of diatomic gas are put together in a container. The molar specific heat (in J K 1 mol 1 ) (A)

18.7

(B)

18.9

VMC/Gasesous State & Thermodynamics

(C)

82

19.2

(D)

None of these

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

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ROLL NO.

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

1 mol of gas occupies a volume of 200 mL at 100 mm pressure. What is the volume occupied by two moles of gas at 400 mm pressure and at same temperature? (A) 50 mL (B) 100 mL (C) 200 mL (D) 400 mL

2.

The molecules of a given mass of a gas have a rms velocity of 200 m/s at 27C and 1.0 105 N / m 2 pressure. When the temperature is 127C and pressure is 0.5 105 N / m 2 , the rms velocity in m/s will be : (A)

3.

100 2

(C)

400 3

(D)

None of these\

9mA = 4mB

(B)

3mA = 2mB

(C)

2mA = 3mB

(D)

4mA = 9mB

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V1 and contains ideal gas at pressure p1 and temperature T1. The other chamber has volume V2 and contains ideal gas at pressure p2 and temperature T2. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be : (A)

5.

(B)

Two identical vessels A and B with frictionless pistons contain the same ideal gas at the same temperature and the same volume V. The masses of gas in A B are mA and mB respectively. The gases are allowed to expand isothermally to same final volume 2 V. The change in pressure of the gas in A and B found to be Δp and 1.5 p respectively. Then: (A)

4.

100 2 3

T1T2 p1V1 p2V2 p1V1T2 p2V2T1

(B)

p1V1T1 p2V2T2 p1V1 p2V2

(C)

p1V1T2 p2V2T1 p1V1 p2V2

(D)

T1T2 p1V1 p2V2 p1V1T1 p2V2T2

The ratio of specific heats of a gas is . The change in internal energy of one mole of the gas, when the volume changes from V to 2V at constant pressure p is: (A)

1 pV

(B)

pV

(C)

pV 1

(D)

pV

6.

In the adiabatic compression, the decrease in volume is associated with (A) increase in temperature and decrease in pressure (B) decrease in temperature and increase in pressure (C) decrease in temperature and decrease in pressure (D) increase in temperature and increase in pressure

7.

An ideal gas expands isothermally. Initial pressure is p1 and final pressure is p3.The total work done is W. Then (A) (B) (C) (D) p3 p1 W 0 p3 p1 W 0 p3 p1 W 0 p3 p1 W 0

8.

Cp 1.4 Adiabatic modulus of elasticity of a gas is 2.1 105 Nm 2 . What will be its isothermal modulus of elasticity ? C V

(A)

1.2 105 Nm 2

(B)

4 105 Nm 2

VMC/Gasesous State & Thermodynamics

(C)

83

1.5 105 Nm 2

(D)

1.8 105 Nm 2

HWT/Physics

Vidyamandir Classes 9.

10.

When water is converted into ice, its entropy : (A) increases (C) remains unchanged

(B) (D)

decreases first decreases and then increases

70 cal of heat is required to raise the temperature of 2 moles of an ideal gas from 30C to 35C while the pressure of the gas is kept constant. The amount of the heat required to raise the temperature of the same gas through the same temperature range at constant volume is (gas constant R = 2cal mol 1 K 1 ) (A)

70 cal

(B)

60 cal

VMC/Gasesous State & Thermodynamics

(C)

84

50 cal

(D)

30 cal

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

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TIME : 25 MINUTES

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

If universal gas constant is R, the essential heat to increase temperature from 273 K to 473 K at constant volume for ideal gas of 4 mol is : (A) 200 R (B) 400 R (C) 800 R (D) 1200 R

2.

An ideal gas ( 1.5 ) is expanded adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of molecules 2.0 times? (A) 4 times (B)

16 times

(C)

8 times

(D)

2 times

3.

If masses of all molecules of a gas are halved and their speeds are doubled, then the ratio of initial and final pressure : (A) 1:2 (B) 2:1 (C) 4:1 (D) 1:4

4.

When a system is taken from state i to state f along the path iaf, it is found that Q = 50 cal and W = 20 cal. Along the path ibf, Q = 36 cal. W along the path ibf is :

5.

(A)

6 cal

(B)

16 cal

(C)

66 cal

(D)

14 cal

A perfect gas goes from state A to another state B by absorbing 8 105 J of heat and doing 6.5 105 J of external work. It is now transferred between the same two states in another process in which it absorbs 105 J of heat in the second process. Then :

6.

(A)

work done on the gas is 0.5 105 J

(B)

work done by gas is 0.5 105 J

(C)

work done on gas is 105 J

(D)

work done by gas is 105 J

1 mm3 of gas is compressed at 1 atm pressure and temperature 27C to 627C . What is the final pressure under adiabatic condition? ( for the gas = 1.5) (A)

7.

27 105 Nm 2

(B)

12 105 Nm 2

(C)

15 105 Nm 2

(D)

23 103 Nm 2

Unit mass of a liquid volume V1 is completely charged into a gas of volume V2 at a constant external pressure p and temperature T. If the latent heat of evaporation for the given mass is L, then the increase in the internal energy of the system is: (A)

8.

zero

(B)

p V2 V1

(C)

L p V2 V1

A Carnot engine operating between temperature T1 and T2 has efficiency 1 . Then T1 and T2 are respectively. 3 (A) 372 K and 330 K (B)

330 K and 268 K

VMC/Gasesous State & Thermodynamics

(C)

85

(D)

L

1 . When T2 is lowered by 62 K, its efficiency increase to 6

310 K and 248 K

(D)

372 K and 310 K

HWT/Physics

Vidyamandir Classes 9.

When you make ice cubes, the entropy of watre (A) does not change (B) increases (C) decreases (D) may either increase or decrease depending on the process used

10.

The temperature of 5 moles of a gas at constant volume is changed from 100C to 120C . The change in internal energy 80J. The total heat capacity of the gas at constant volume will be in JK 1 is: (A) 8 (B) 4 (C) 0.8

VMC/Gasesous State & Thermodynamics

86

(D)

0.4

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

TEST CODE : GST [6]

ROLL NO.

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This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

An ideal gas is expanding such that pT2 = constant. The coefficient of volume expansion of the gas is : 1 2 3 4 (A) (B) (C) (D) T T T T The rms velocity of gas molecules is 300ms 1 . The rms velocity of molecules of gas with twice the molecular weight and half the absolute temperature is : (A)

300 ms 1

(B)

600 ms 1

(C)

75ms 1

(D)

150 ms 1

3.

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

4.

A thermodynamical system is changed from state (p1, V1) to (p2, V2) by two different process, quantity which will remain same will be : ΔQ (A) (B) ΔW (C) (D) ΔQ ΔW ΔQ ΔW

5.

The p–V diagram of a system undergoing thermodynamic transformation is shown in figure. The work done by the system in going from A B C is 30 J, and 40 J heat is given to the system. The change in internal energy between A and C is: (A) 10 J (B) 70 J (C) 84 J (D) 134 J

6.

A monoatomic gas is suddenly compressed to (1/8)th of its initial volume. The ratio of its final pressure to the initial pressure is (Given the ratio of the specific heats of the given gas to be 5/3) (A) 32 (B) 40/3 (C) 24/8 (D) 8

7.

A given mass of a gas is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restored and is pressure is then found to be 0.75 of its initial pressure. The ratio of the specific heats of the gas is approximately. (A) 1.20 (B) 1.41 (C) 1.67 (D) 1.83

8.

A Carnot engine whose efficiency is 40% , receives heat at 500 K. If the efficiency is to be 50% , the source temperature for the same exhaust temperature is: (A) 900 K (B) 600 K (C) 700 K (D) 800 K

9.

An ideal heat engine exhausting at 27C is to have 25% efficiency. It must take heat at (A)

10.

127C

(B)

227C

(C)

327C

(D)

None of these

At what temperature the rms velocity of helium molecules will be equal to that of hydrogen molecules at NTP? (A) 844 K (B) 64 K (C) 273C (D) 273 K

VMC/Gasesous State & Thermodynamics

87

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

TEST CODE : GST [7]

ROLL NO.

START TIME :

STUDENT’S SIGNATURE :

END TIME :

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PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. However, questions marked with ‘*’ may have More than One correct option. 1.

One litre of oxygen at a pressure of 1 atm and two litres of nitrogen at a pressure of 0.5 atm, are introduced into a vessel of volume 1L. If there is no change in temperature, the final pressure of the mixture of gas (in atm) is: (A) 1.5 (B) 2.5 (C) 2 (D) 4

2.

The ratio of the vapour densities of two gases at a given temperature is 9 : 8. The ratio of the rms velocities of their molecules is: (A)

3.

32 2

(B)

2 2 3

(C)

9:8

`

(D)

8:9

The temperature of a gas is 68C . At what temperature will the average kinetic energy of its molecules be twice that of at

68C ? (A)

130C

(B)

127C

(C)

100C

(D)

105C

4.

310 J of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 25C to 35C . The amount of heat required to rise the temperature of the gas through the same range at constant volume is : (A) 384 J (B) 144 J (C) 276 J (D) 425 J

5.

A sample of ideal monoatomic gas is taken round the cycle ABCA as shown in the figure. The work done during the cycle is :

6.

(A)

3 pV

(B)

zero

(C)

9 pV

(D)

6pV

Ideal gas undergoes an adiabatic change in its state from (p1, V1, T1) to (p2, V2, T2). The work done (W) in the process is ( = number of molecules, Cp, and CV are molar specific heats of gas)

7.

(A)

W C p T1 T2

(B)

W CV T1 T2

(C)

W CP T1 T2

(D)

W CV T1 T2

7 The pressure and density of a diatomic gas change adiabatically from 5

should be: (A) 16 8.

(B)

32

(C)

64

p1 1

to

(D)

p2 2 . If

2 p 32 , then 2 1 p1

128

A diatomic ideal gas is used in a car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from V to 32V. The efficiency of the engine is: (A) 0.5 (B) 0.75 (C) 0.99 (D) 0.25

VMC/Gasesous State & Thermodynamics

88

HWT/Physics

Vidyamandir Classes 9.

The sink temperature of a heat engine 77C . The efficiency is 30% . The source temperature is: (A)

10.

500C

(B)

227C

(C)

317C

(D)

427C

Four molecules of a gas have speeds 1, 2, 3 and 4kms 1 . The value of rms speed of the gas molecules is ; (A)

1 15 kms 1 2

(B)

1 10 kms 1 2

VMC/Gasesous State & Thermodynamics

(C)

89

25kms 1

(D)

15 kms 1 2

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

TEST CODE : GST [8]

ROLL NO.

START TIME :

STUDENT’S SIGNATURE :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

Volume-temperature graph at atmospheric pressure for a monoatomic gas (V in m3, T in C ) is:

(A)

2.

(B)

(C)

(D)

If the rms velocity of a gas is v, then : (A)

v 2T = constant

(B)

v 2 / T constant (C)

vT2 = constant

(D)

v is independent of T

3.

One mole of a monatomic ideal gas is mixed with one mole of a diatomic ideal gas. The molar specific heat of the mixture at constant volume is: (A) (3/2) R (B) (5 / 2) R (C) 2R (D) 4R

4.

Two cylinder A and B fitted with pistons, contain equal number of moles of an ideal monoatomic gas at 400 K. The piston of A is free to move while that of B is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in A is 42 K, the rise in temperature of the gas in B is ( 5 / 3 ) (A)

25.2 K

(B)

35 K

(C)

42 K

(D)

70 K

5.

5.6 of helium gas at STP is adiabatically compressed to 0.7 L. Taking the initial temperature of be T1, the work done in the process is : 9 3 15 9 RT1 RT1 RT1 RT1 (A) (B) (C) (D) 8 2 8 2

6.

The work of 146 kJ is performed in order to compress one kilo mole of a gas adiabatically and in this process the temperature of the gas increases by 7C . The gas is ( R 8.3J mol 1K 1 ) (A) (C)

7.

diatomic a mixture of monotomic and diatomic

(B) (D)

triatomic monoatomic

Ten moles of an ideal gas at constant temperature 500 K is compressed from 50 L to 5 L. Work done in the process is (Given, R = 8.31 J mol 1K 1 ) (A)

8.

1.2 104 J

(B)

2.4 104 J

(C)

4.8 104 J

(D)

9.6 104 J

The efficiency of Carnot’s heat engine is 0.5, when the temperature of the source is T1 and that of sink is T2. The efficiency of another Carnot’s heat engine is also 0.5. The temperature of source and sink of the second engine are respectively. T 2T1 2 (A) (B) (C) (D) 2T1 2T2 T1 5 T2 5 T1 10T2 10 2

VMC/Gasesous State & Thermodynamics

90

HWT/Physics

Vidyamandir Classes 9.

A Carnot engine takes heat from a reservoir at 627C and rejects heat to a sink at 27C . Its efficiency will be : (A) 3/5 (B) 1/3 (C) 2/3 (D) 200/209

10.

To what temperature should the hydrogen at 327C be cooled at constant pressure, so that the root mean square velocity of its molecules becomes half of its previous value? (A) 123C (B) 123C (C) 100C (D) 0C

VMC/Gasesous State & Thermodynamics

91

HWT/Physics

Vidyamandir Classes

DATE :

MARKS : 10

IITJEE :

NAME :

TIME : 25 MINUTES

TEST CODE : GST [9]

ROLL NO.

START TIME :

END TIME :

STUDENT’S SIGNATURE :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

A bubble is at the bottom of the lake of depth h. As the bubble comes to sea level, its radius increases three times. If atmospheric pressure is equal to l meter of water column, then h is equal to : (A) 26l (B) l (C) 25l (D) 30l

2.

KE per unit volume is E. The pressure exerted by the gas is given by : E 2E 3E (A) (B) (C) 3 3 2

3.

5.

E 2

5 7 If one mole of a monoatomic gas is mixed with one mole of a diatomic gas , the value of for the mixture is : 3 5

(A) 4.

(D)

1.40

(B)

1.50

(C)

1.53

(D)

3.07

An ideal gas expands along the path AB as shown in the p-V diagram. The work done is : (A)

4 104 J

(B)

1.2 105 J

(C) (D)

2.4 105 J None of the above

An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume : ( 1, 4 and 21.4 0.38 ). The ratio of the final to initial pressure is : (A)

0.76 : 1

(B)

1:1

(C)

0.66 : 1

(D)

0.86 : 1

6.

During an adiabatic process, the cube of the pressure is found to be inversely proportional to the fourth power of the volume. Then the ratio of specific heat is : (A) 1 (B) 1.33 (C) 1.67 (D) 1.4

7.

During an isothermal expansion of an ideal gas : (A) its internal energy decreases (B) its internal energy does not change (C) The work done by the gas is equal to the quantity of heat absorbed by it : (D) Both (B) and (C) are correct

8.

Three designs are proposed for an engine operating between 500 K and 300 K. For 1 kcal of heat input, design A claims to produce 3000 J of work, design B claims to produce 2000 J of work and design C claims to produce 1680 J of work. The design which is possible (A) A only (B) B only (C) C only (D) All of these

VMC/Gasesous State & Thermodynamics

92

HWT/Physics

Vidyamandir Classes 9.

A Carnot engine, having an efficiency of 1 / 10 as heat engine, is used as a refrigerator. If the work done on the system 10 J, the amount energy absorbed from the reservoir at lower temperature is : (A) 99 J (B) 90 J (C) 1J

10.

(D)

100 J

In a Carnot engine, when T2 0C and T1 200C , its efficiency is 1 and when T1 0C T2 200C , its efficiency is 2 , then what is 1 / 2 , then what is 1 / 2 ? (A)

0.577

(B)

0.733

VMC/Gasesous State & Thermodynamics

(C)

93

0.638

(D)

Cannot be calculated

HWT/Physics

Vidyamandir Classes

DATE :

IITJEE :

NAME :

MARKS : 10

TIME : 25 MINUTES

TEST CODE : GST [10]

ROLL NO.

START TIME :

STUDENT’S SIGNATURE :

END TIME :

TIME TAKEN:

PARENT’S SIGNATURE :

This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.

2.

Two gases A and B having same pressure p, volume V and absolute temperature T are mixed. If the mixture has the volume and temperature as V and T respectively, then the pressure of the mixture is: (A) 2p (B) p (C) p/2 (D) 4p One kg of a diatomic gas is at a pressure of 8 104 Nm 2 . The density of the gas is 4kgm 3 . What is the energy of the gas due to its thermal motion? (A)

3.

(B)

6 104 J

(D)

7 104 J

R (B) (C) (D) CV R CV 2 R CV 3R 2 1 cm3 of water at its boiling point absorbs 540 cal of heat of become steam with a volume of 1671 cm3. If the atmospheric

Nm 2 and the mechanical equivalent of heat = 419 J cal 1 , the energy spent in this process in

overcoming intermolecular force is : (A) 540 cal (B)

6.

(C)

CV

pressure = 1.013 105

5.

5 104 J

For a gas molecule with 6 degrees of freedom the law of equipartition of energy gives the following relation between the molecular specific heat (CV) and gas constant (R) : (A)

4.

3 104 J

40 cal

(C)

500 cal

(D)

zero

One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is p0. Choose the correct option (s) from the following : (A) Internal energies at A and B are the same (B) Work done by the gas in process AB in p0V0 In 4 p0 4

(C)

Pressure at C is

(D)

T Temperature at C is 0 4

One mole of an ideal gas at an initial temperature of T Kelvin does 6R joule of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is 5/3, the final temperature of gas will be : (A)

(T + 2.4) K

(B)

T 2 .4 K

(C)

T 4 K

(D)

T 4 K

7.

A container having 1 mole of a gas at a temperature 27C has a movable piston which maintains at constant pressure in container of 1 atm. The gas is compressed until temperature becomes 127°C. The work done is (Cp for gas is 7.03 cal/mol – K) (A) 703 J (B) 814 J (C) 121 J (D) 2035 J

8.

A Carnot engine working between 450 K and 600 K has a work output of 300 J/cycle. The amount of heat energy supplied to the engine from the source in each cycle is : (A) 400 J (B) 800 J (C) 1600 J (D) 1200 J

VMC/Gasesous State & Thermodynamics

94

HWT/Physics

Vidyamandir Classes 9.

A Carnot’s engine operates with source at 127C and sink at 27C . If the source supplies 40 kJ of heat energy, the work done by the engine is : (A) 30 kJ (B) 10 kJ (C) 4 kJ (D) 1 kJ

10.

A Carnot engine takes 3 106 cal of heat form a reservoir at 627C and gives it to a sink at 27C . The work done by the engine is : (A)

4.2 106 J

(B)

8.4 106

VMC/Gasesous State & Thermodynamics

(C)

95

1.68 106 J

(D)

zero

HWT/Physics

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