# JEE Main

Explore popular questions from Behaviour of Perfect Gas and Kinetic Theory for JEE Main. This collection covers Behaviour of Perfect Gas and Kinetic Theory previous year JEE Main questions hand picked by experienced teachers.

# Mathematics

Behaviour of Perfect Gas and Kinetic Theory

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Q 1. A cylinder of fixed capacity 44.8 litre, contains a monatomic gas at standard temperature and pressure. The amount of heat required to cylinder by {tex} \small 10 ^ { \circ } \mathrm { C } {/tex} will be. {tex} \small( R = {/tex} universal gas constant)

A

{tex} R {/tex}

B

{tex} 10 R {/tex}

C

{tex} 20 R {/tex}

{tex} 30 R {/tex}

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Q 2. An air bubble doubles its radius on raising from the bottom of water reservoir to be the surface of water in it. If the atmospheric pressure is equal to {tex} 10 { m } {/tex} of water, the height of water in the reservoir is A

{tex} 10 m {/tex}

B

{tex} 20 m {/tex}

{tex} 70 m {/tex}

D

{tex} 80 m {/tex}

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Q 3. Pressure versus temperature graphs of an ideal gas are as shown in figure. Choose the wrong statement A

Density of gas is increasing in graph (i)

B

Density of gas is decreasing in graph (ii)

Density of gas is constant in graph (iii)

D

None of these

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Q 4. An ideal gas has an initial pressure of 3 pressure units and an initial volume of 4 volume units. The table gives the final pressure and volume of the gas (in those same units) in four, processes. Which processes start and end on the same isotherm A

{tex} A {/tex}

B

{tex} B {/tex}

{tex} C {/tex}

D

{tex} D {/tex}

##### Explanation so, final {tex}{ P }{ V }=12{/tex} Hence, option C is correct.

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Q 5. Suppose ideal gas equation {tex} V {/tex} follows {tex} 3VP = constant{/tex}. Initial temperature and volume of the gas are {tex} T {/tex} and {tex} V {/tex} respectively. If gas expand to {tex} 27\ V {/tex} then its temperature will be come

A

{tex} T {/tex}

{tex} 9 \ T {/tex}

C

{tex} 27 \ T {/tex}

D

{tex} T / 9 {/tex}

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Q 6. One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas. The molar specific heat of the mixture at constant volume is

A

{tex} 8 {/tex}

B

{tex} \frac { 3 } { 2 } \ R {/tex}

{tex} 2\ R {/tex}

D

{tex} 2.5\ R {/tex}

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Q 7. 2 mole of an ideal monoatomic gas mix with 1 mole of a ideal diatomic gas. The for the mixture is -

A  C D

None

##### Explanation = +  = 3 +  = γmin-1 = γmin = + 1 = Correct Marks 4

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Q 8. A vessel contains 1 mole of O2 gas (molar mass 32) at a temperature T. The pressure of the gas is P. An identical vessel containing one mole of He gas (molar mass 4) at a temperature 2T has a pressure of -

A

P/8

B

P

2P

D

8P

##### Explanation

P1V = n1RT ; P2V = n2R2T  ⇒ P2 = 2P

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Q 9. When the temperature of a gas is raised from {tex} 27 ^ { \circ } \mathrm { C } {/tex} to {tex} 90 ^ { \circ } \mathrm { C } , {/tex} the percentage increase in the {tex} r . m .s {/tex} velocity of the molecules will be

{tex} 10 \% {/tex}

B

{tex} 15 \% {/tex}

C

{tex} 20 \% {/tex}

D

{tex} 17.5 \% {/tex}

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Q 10. A gas is enclosed in a closed pot. On keeping this pot in a train moving with high speed, the temperature of the gas

A

Will increase

B

Will decrease

Will remain the same

D

Will change according to the nature of the gas

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Q 11. Two spherical vessel of equal volume, are connected by a{tex} \ \ n {/tex} arrow tube. The apparatus contains an ideal gas at one atmosphere and {tex} 300 K {/tex}. Now if one vessel is immersed in a bath of constant temperature {tex} 600 K {/tex} and the other in a bath of constant temperature {tex} 300 K {/tex}. Then the common pressure will be A

{tex}1atm {/tex}

B

{tex} \frac { 4 } { 5 } a t m {/tex}

{tex} \frac { 4 } { 3 } a t m {/tex}

D

{tex} \frac { 3 } { 4 } a t m {/tex}

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Q 12. The {tex} r . m .s {/tex} velocity of a gas at a certain temperature is {tex} \sqrt { 2 } {/tex} times than that of the oxygen molecules at that temperature. The gas can be

A

{tex} H _ { 2 } {/tex}

B

{tex} H e {/tex}

{tex} C H _ { 4 } {/tex}

D

{tex} S O _ { 2 } {/tex}

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Q 13. At what temperature, the mean kinetic energy of {tex} O _ { 2 } {/tex} will be the same for {tex} H _ { 2 } {/tex} molecules at {tex} - 73 ^ { \circ } \mathrm { C } {/tex}

A

{tex} 127 ^ { \circ } \mathrm { C } {/tex}

B

{tex} 527 ^ { \circ } \mathrm { C } {/tex}

{tex} - 73 ^ { \circ } \mathrm { C } {/tex}

D

{tex} - 173 ^ { \circ } \mathrm { C } {/tex}

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Q 14. The volume of a gas at pressure {tex} 21 \times 10 ^ { 4 } N / m ^ { 2 } {/tex} and temperature {tex} 27 ^ { \circ } \mathrm { C } {/tex} is 83 litres. If {tex} R = 8.3\ J/ \mathrm { mol } / \mathrm { K } {/tex}, then the quantity of gas in {tex} \mathrm { gm-mole } {/tex} will be

A

15

B

42

7

D

14

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Q 15. The pressure and temperature of an ideal gas in a closed vessel are {tex} 720\ { kPa } {/tex} and {tex} 40 ^ { \circ } { C } {/tex} respectively. If {tex} \frac { 1 } { 4 } {/tex} th of the gas is released from the vessel and the temperature of the remaining gas is raised to {tex} 353 ^ { \circ }{ C } , {/tex} the final pressure of the gas is

A

{tex} 1440 \mathrm { kPa } {/tex}

{tex} 1080 \mathrm { kPa } {/tex}

C

{tex} 720 \mathrm { kPa } {/tex}

D

{tex} 540 \mathrm { kPa } {/tex}

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Q 16. If the {tex} r . m .s {/tex} velocity of a gas at a given temperature (Kelvin scale) is {tex} 300 \mathrm { m } / \mathrm { sec } . {/tex} What will be the {tex} \mathrm { r.m.s } {/tex} velocity of a gas having twice the molecular weight and half the temperature on Kelvin scale =

A

{tex} 300 \mathrm { m } / \mathrm { sec } {/tex}

B

{tex} 600 \mathrm { m } / \mathrm { sec } {/tex}

C

{tex} 75 \mathrm { m } / \mathrm { sec } {/tex}

{tex} 150 \mathrm { m } / \mathrm { sec } {/tex}

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Q 17. The ratio of two specific heats {tex} \frac { C _ { P } } { C _ { V } } {/tex} of {tex} C O {/tex} is

A

1.33

1.4

C

1.29

D

1.66

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Q 18. The energy of a gas/litre is 300 joules, then its pressure will be

A

{tex} 3 \times 10 ^ { 5 } \mathrm { N } / \mathrm { m } ^ { 2 } {/tex}

B

{tex} 6 \times 10 ^ { 5 } \mathrm { N } / \mathrm { m } ^ { 2 } {/tex}

C

{tex} 10 ^ { 5 } \mathrm { N } / \mathrm { m } ^ { 2 } {/tex}

{tex} 2 \times 10 ^ { 5 } \mathrm { N } / \mathrm { m } ^ { 2 } {/tex}

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Q 19. If pressure of {tex} C O _ { 2 } {/tex} (real gas) in a container is given by {tex} P = \frac { R T } { 2 V - b } - \frac { a } { 4 b ^ { 2 } } {/tex} then mass of the gas in container is

A

{tex}11 \ g m {/tex}

{tex} 22 \ g m {/tex}

C

{tex} 33 \ gm {/tex}

D

{tex} 44 \ gm {/tex}

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Q 20. A pressure cooker contains air at 1 atm and {tex} 30 ^ { \circ } \mathrm { C } {/tex}. If the safety value of the cooler blows when the inside pressure {tex} \geq 3\ atm {/tex} , then the maximum temperature of the air, inside the cooker can be

A

{tex} 90 ^ { \circ } \mathrm { C } {/tex}

{tex} 636 ^ { \circ } \mathrm { C } {/tex}

C

{tex} 909 ^ { \circ } \mathrm { C } {/tex}

D

{tex} 363 ^ { \circ } \mathrm { C } {/tex}

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Q 21. One mole of an ideal monatomic gas requires {tex}210\ J{/tex} heat to raise the temperature by {tex} 10 K , {/tex} when heated at constant temperature. If the same gas is heated at constant volume to raise the temperature by {tex}10 K {/tex} then heat required is

A

{tex} 238\ J {/tex}

{tex} 126\ J {/tex}

C

{tex} 210 \ J{/tex}

D

{tex}350\ J{/tex}

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Q 22. From the following {tex} V - T {/tex} diagram we can conclude A

{tex} P_{1} = P_{2} {/tex}

{tex} P_{1} > P_{2} {/tex}

C

{tex} P_{1}< P_{2} {/tex}

D

None of these

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