JEE Main > Behaviour of Perfect Gas and Kinetic Theory

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 popular teachers.


Q 1.    

Correct4

Incorrect-1

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

Q 2.    

Correct4

Incorrect-1

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}

Explanation


Q 3.    

Correct4

Incorrect-1

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}

Explanation

Q 4.    

Correct4

Incorrect-1

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}

Explanation

Q 5.    

Correct4

Incorrect-1

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

Explanation

Q 6.    

Correct4

Incorrect-1

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}

Explanation

Q 7.    

Correct4

Incorrect-1

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}

Explanation

Q 8.    

Correct4

Incorrect-1

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}

Explanation

Q 9.    

Correct4

Incorrect-1

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

Explanation

Q 10.    

Correct4

Incorrect-1

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}

Explanation

Q 11.    

Correct4

Incorrect-1

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}

Explanation

Q 12.    

Correct4

Incorrect-1

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}

Explanation

Q 13.    

Correct4

Incorrect-1

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

Explanation

Q 14.    

Correct4

Incorrect-1

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}

Explanation

Q 15.    

Correct4

Incorrect-1

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}

Explanation

Q 16.    

Correct4

Incorrect-1

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

A

{tex} R {/tex}

B

{tex} 10 R {/tex}

C

{tex} 20 R {/tex}

{tex} 30 R {/tex}

Explanation

Q 17.    

Correct4

Incorrect-1

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}

Explanation

Q 18.    

Correct4

Incorrect-1

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}

Explanation

Q 19.    

Correct4

Incorrect-1

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

Explanation



Q 20.    

Correct4

Incorrect-1

A cylinder contains {tex} 10 \mathrm { kg } {/tex} of gas at pressure of {tex} 10 ^ { 7 } \mathrm { N } / \mathrm { m } ^ { 2 } . {/tex} The quantity of gas taken out of the cylinder, if final pressure is {tex} 2.5 \times 10 ^ { 6 } \mathrm { N } / \mathrm { m } ^ { 2 } , {/tex} will be (Temperature of gas is constant)

A

{tex} 15.2 \mathrm { kg } {/tex}

B

{tex} 3.7 \mathrm { kg } {/tex}

C

Zero

{tex} 7.5 \mathrm { kg } {/tex}

Explanation

Q 21.    

Correct4

Incorrect-1

Certain amount of an ideal gas are contained in a closed vessel. The vessel is moving with a constant velocity {tex} v {/tex}. The molecular mass of gas is {tex} M {/tex}. The rise in temperature of the gas when the vessel is suddenly stopped is {tex} \left( \gamma = C _ { P } / C _ { V } \right) {/tex}

A

{tex} \frac { M v ^ { 2 } } { 2 R ( \gamma + 1 ) } {/tex}

{tex} \frac { M v ^ { 2 } ( \gamma - 1 ) } { 2 R } {/tex}

C

{tex} \frac { M v ^ { 2 } } { 2 R ( \gamma + 1 ) } {/tex}

D

{tex} \frac { M v ^ { 2 } } { 2 R ( \gamma + 1 ) } {/tex}

Explanation

Q 22.    

Correct4

Incorrect-1

Air is filled at {tex} 60 ^ { \circ } \mathrm { C } {/tex} in a vessel of open mouth. The vessel is heated to a temperature {tex} T {/tex} so that {tex} 1 / 4 \mathrm { th } {/tex} part of air escapes. Assuming the volume of the vessel remaining constant, the value of {tex} T {/tex} is

A

{tex} 80 ^ { \circ } \mathrm {C} {/tex}

B

{tex} 444 ^ { \circ } \mathrm { C } {/tex}

C

{tex} 333 ^ { \circ } \mathrm { C } {/tex}

{tex} 171 ^ { \circ } \mathrm { C } {/tex}

Explanation

Q 23.    

Correct4

Incorrect-1

A partition divides a container having insulated walls into two compartments I. and II . the same gas fills the two compartments. The ratio of the number of molecules in compartments I. and II. is

A

1: 6

B

6: 1

C

4:1

1: 4

Explanation

Q 24.    

Correct4

Incorrect-1

Considering the gases to be ideal, the value of {tex} \gamma = \frac { C _ { P } } { C _ { V } } {/tex} for a gaseous mixture consisting of {tex} = 3 {/tex} moles of carbon dioxide and 2 moles of oxygen will be {tex} \left( \gamma _ { O _ { 2 } } = 1.4 , \gamma _ { C O _ { 2 } } = 1.3 \right) {/tex}

A

1.37

1.34

C

1.55

D

1.63

Explanation

Q 25.    

Correct4

Incorrect-1

A jar has a mixture of hydrogen and oxygen gas in the ratio of {tex} 1: 5 . {/tex} The ratio of mean kinetic energies of hydrogen and oxygen molecules is

A

1: 16

B

1: 4

C

1: 5

1: 1

Explanation