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JEE Advanced > Behaviour of Perfect Gas and Kinetic Theory

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

Q 1.

Correct4

Incorrect-1

In an adiabatic process, the root mean square speed of the molecules of a monoatomic gas becomes twice its initial value. The ratio of the initial volume of the gas to the final volume is

A

{tex}2{/tex}

B

{tex} 2 ^ { 3 / 2 } {/tex}

C

{tex}4{/tex}

{tex}8{/tex}

Explanation

Q 2.

Correct4

Incorrect-1

The root mean square speed of hydrogen molecules at a certain temperature is {tex} v {/tex}. If the temperature is doubled and the hydrogen gas dissociates into atomic hydrogen, the rms speed will become

A

{tex} \frac { v } { 4 } {/tex}

B

{tex} \frac { v } { 2 } {/tex}

{tex} 2 v {/tex}

D

{tex} 4 v {/tex}

Explanation

Q 3.

Correct4

Incorrect-1

A gas in a closed container has temperature {tex} T {/tex} and pressure {tex} P . {/tex} If the molecules of the gas undergo inelastic collisions with the walls of the container, then

A

both {tex} P {/tex} and {tex} T {/tex} will decrease

B

{tex} P {/tex} decreases and {tex} T {/tex} increases

C

{tex} P {/tex} increases and {tex} T {/tex} decreases

both {tex} P {/tex} and {tex} T {/tex} remain the same

Explanation


Q 4.

Correct4

Incorrect-1

Two moles of hydrogen are mixed with {tex} n {/tex} moles of helium. The root mean square speed of the gas molecules in the mixture is {tex} \sqrt { 2 } {/tex} times the speed of sound in the mixture. The value of {tex} n {/tex} is

A

1

2

C

3

D

4

Explanation


Q 5.

Correct4

Incorrect-1

A vessel contains {tex} 4 {/tex} moles of oxygen and {tex} 2 {/tex} moles of argon at absolute temperature {tex} T {/tex}. The total internal energy of the gas mixture is

A

{tex} 6 R T {/tex}

B

{tex} 9 R T {/tex}

C

{tex} 11 R T {/tex}

{tex} 13 R T {/tex}

Explanation

Q 6.

Correct4

Incorrect-1

The average translational kinetic energy of a molecule of a gas at absolute temperature {tex} T {/tex} is proportional to

A

{tex} \frac { 1 } { T } {/tex}

B

{tex} \sqrt { T } {/tex}

{tex} T {/tex}

D

{tex} T ^ { 2 } {/tex}

Explanation

Q 7.

Correct4

Incorrect-1

The root mean square speed of the molecules of an enclosed gas is {tex} v {/tex}. What will be the root mean square speed if the pressure is doubled, the temperature remaining the same?

A

{tex} v / 2 {/tex}

{tex} v {/tex}

C

{tex} 2 v {/tex}

D

{tex} 4 v {/tex}

Explanation

Q 8.

Correct4

Incorrect-1

The mass of an oxygen molecule is about {tex}16{/tex} times that of a hydrogen molecule. At room temperature the rms speed of oxygen molecules is {tex} v {/tex}. The rms speed of the hydrogen molecule at the same temperature will be

A

{tex} v / 16 {/tex}

B

{tex} v / 4 {/tex}

{tex} 4 v {/tex}

D

{tex} 16 v {/tex}

Explanation

Q 9.

Correct4

Incorrect-1

The average kinetic energy of hydrogen molecules at {tex} 300 \mathrm { K } {/tex} is {tex} E {/tex}. At the same temperature, the averages kinetic energy of oxygen molecules will be

A

{tex} E / 16 {/tex}

B

{tex} E / 4 {/tex}

{tex} E {/tex}

D

{tex} 4 E {/tex}

Explanation

Q 10.

Correct4

Incorrect-1

At room temperature {tex} \left( 27 ^ { \circ } \mathrm { C } \right) {/tex} the rms speed of the molecules of a certain diatomic gas is found to be {tex} 1920 \mathrm { ms } ^ { - 1 } {/tex}. The gas is

{tex} \mathrm { H } _ { 2 } {/tex}

B

{tex} \mathrm { F } _ { 2 } {/tex}

C

{tex} \mathrm { O } _ { 2 } {/tex}

D

{tex} \mathrm { Cl } _ { 2 } {/tex}

Explanation

Q 11.

Correct4

Incorrect-1

The temperature of an ideal gas is increased from {tex} 120 \mathrm { K } {/tex} to {tex} 480 \mathrm { K } {/tex}. If at {tex} 120 \mathrm { K } {/tex}, the root mean square speed of the gas molecules is {tex} v {/tex}, then at {tex} 480 \mathrm { K } {/tex} it will be

A

{tex} 4 v {/tex}

{tex} 2 v {/tex}

C

{tex} \frac { v } { 2 } {/tex}

D

{tex} \frac { v } { 4 } {/tex}

Explanation

Q 12.

Correct4

Incorrect-1

Three closed vessels {tex} \mathrm {A , B} {/tex} and {tex} \mathrm C {/tex} are at the same temperature. Vessel {tex} \mathrm A {/tex} contains only {tex} \mathrm { O } _ { 2 } , \mathrm B {/tex} only {tex} \mathrm { N } _ { 2 } {/tex} and {tex} \mathrm C {/tex} a mixture of equal quantities of {tex} \mathrm { O } _ { 2 } {/tex} and {tex} \mathrm { N } _ { 2 } {/tex}. If the average speed of {tex} \mathrm { O } _ { 2 } {/tex} molecules in vessel {tex} \mathrm A {/tex} is {tex} v _ { 1 } , {/tex} that of {tex} \mathrm { N } _ { 2 } {/tex} molecules in vessel {tex} \mathrm B {/tex} is {tex} v _ { 2 } , {/tex} the average speed of {tex} \mathrm { O } _ { 2 } {/tex} molecules in vessel {tex} \mathrm C {/tex} is

A

{tex} \frac { 1 } { 2 } \left( v _ { 1 } + v _ { 2 } \right) {/tex}

{tex} v _ { 1 } {/tex}

C

{tex} \sqrt { v _ { 1 } v _ { 2 } } {/tex}

D

{tex} \sqrt { \frac { 3 k T } { M } } {/tex}

Explanation

Q 13.

Correct4

Incorrect-1

The average translational energy and the rms speed of molecules of a sample of oxygen gas at {tex} 300 \mathrm { K } {/tex} are {tex} 6.21 \times 10 ^ { - 21 } \mathrm { J } {/tex} and {tex} 484 \mathrm { ms } ^ { - 1 } {/tex} respectively. The corresponding values at {tex} 600 \mathrm { K } {/tex} are nearly (assuming ideal gas behaviour)

A

{tex} 12.42 \times 10 ^ { - 21 } \mathrm { J } , 968 \mathrm { ms } ^ { - 1 } {/tex}

B

{tex} 8.78 \times 10 ^ { - 21 } \mathrm { J } , 684 \mathrm { ms } ^ { - 1 } {/tex}

C

{tex} 6.21 \times 10 ^ { - 21 } \mathrm { J } , 968 \mathrm { ms } ^ { - 1 } {/tex}

{tex} 12.42 \times 10 ^ { - 21 } \mathrm { J } , 684 \mathrm { ms } ^ { - 1 } {/tex}

Explanation

Q 14.

Correct4

Incorrect-1

A vessel contains {tex} 1 {/tex} mole of {tex} \mathrm { O } _ { 2 } {/tex} gas (molar mass {tex} 32 {/tex}) at a temperature {tex} T {/tex}. The pressure of the gas is {tex} P {/tex}. An identical vessel containing one mole of {tex} \mathrm {He} {/tex} gas (molar mass {tex} 4 {/tex} ) at a temperature {tex} 2 T {/tex} has a pressure of

A

{tex} \frac { P } { 8 } {/tex}

B

{tex} P {/tex}

{tex} 2 P {/tex}

D

{tex} 8 P {/tex}

Explanation

Q 15.

Correct4

Incorrect-1

A vessel contains a mixture of 1 mole of oxygen and two moles of nitrogen at {tex} 300 \mathrm { K } {/tex}. The ratio of the rotational kinetic energy per {tex} \mathrm { O } _ { 2 } {/tex} molecule to that per {tex} \mathrm { N } _ { 2 } {/tex} molecule is

{tex}1:1{/tex}

B

{tex}1:2{/tex}

C

{tex}2:1{/tex}

D

depends on the moment of inertia of the two molecules.

Explanation

Q 16.

Correct4

Incorrect-1

Two thermally insulated vessels 1 and 2 are filled with air at temperature {tex} \left( T _ { 1 } , T _ { 2 } \right) , {/tex} volume {tex} \left( V _ { 1 } , V _ { 2 } \right) {/tex} and pressure {tex} \left( P _ { 1 } , P _ { 2 } \right) {/tex} respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

A

{tex} T _ { 1 } + T _ { 2 } {/tex}

B

{tex} \left( T _ { 1 } + T _ { 2 } \right) / 2 {/tex}

{tex} T _ { 1 } T _ { 2 } \left( P _ { 1 } V _ { 1 } + P _ { 2 } V _ { 2 } \right) / \left( P _ { 1 } V _ { 1 } T _ { 2 } + P _ { 2 } V _ { 2 } T _ { 1 } \right) {/tex}

D

{tex} T _ { 1 } T _ { 2 } \left( P _ { 1 } V _ { 1 } + P _ { 2 } V _ { 2 } \right) / \left( P _ { 1 } V _ { 1 } T _ { 1 } + P _ { 2 } V _ { 2 } T _ { 2 } \right) {/tex}

Explanation



Q 17.

Correct4

Incorrect-1

If the temperature of a gas is increased from {tex} 27 ^ { \circ } \mathrm { C } {/tex} to {tex} 927 ^ { \circ } \mathrm { C } , {/tex} the root mean square speed of its molecules

A

becomes half

is doubled

C

becomes 4 times

D

remains unchanged

Explanation

Q 18.

Correct4

Incorrect-1

At what temperature will oxygen molecules have the same root mean square speed as hydrogen molecules at {tex} 200 \mathrm { K } ? {/tex}

A

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

B

{tex} 1327 ^ { \circ } \mathrm { C } {/tex}

C

{tex} 2127 ^ { \circ } \mathrm { C } {/tex}

{tex} 2927 ^ { \circ } \mathrm { C } {/tex}

Explanation