# NEET

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

## Biology

Behaviour of Perfect Gas and Kinetic Theory

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Q 1. The absolute temperature of a gas is increases 3 times. The root mean square velocity of the molecules increases

A

3 times

B

9 times

C

1{tex} / 3 {/tex} times

{tex} \sqrt { 3 } {/tex} times

##### Explanation

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Q 2. Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as {tex} \mathrm { V } ^ { q } {/tex} , where {tex} \mathrm { V } {/tex} is the volume of the gas. The value of {tex} \mathrm { q } {/tex} is : {tex} \left( \gamma = \frac { \mathrm { C } _ { \mathrm { p } } } { \mathrm { C } _ { \mathrm { v } } } \right) {/tex}

{tex} \frac { \gamma + 1 } { 2 } {/tex}

B

{tex} \frac { \gamma - 1 } { 2 } {/tex}

C

{tex} \frac { 3 \gamma + 5 } { 6 } {/tex}

D

{tex} \frac { 3 \gamma - 5 } { 6 } {/tex}

##### Explanation

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Q 3. One kg of a diatomic gas is at a pressure of {tex} 8 \times 10 ^ { 4 } \mathrm { N } / \mathrm { m } ^ { 2 } . {/tex} Th density of the gas is {tex} 4 \mathrm { kg } / \mathrm { m } ^ { 3 } . {/tex} What is the energy of the ga due to its thermal motion?

{tex} 5 \times 10 ^ { 4 } \mathrm { J } {/tex}

B

{tex} 6 \times 10 ^ { 4 } \mathrm { J } {/tex}

C

{tex} 7 \times 10 ^ { 4 } \mathrm { J } {/tex}

D

{tex} 3 \times 10 ^ { 4 } J {/tex}

##### Explanation

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Q 4. A thermally insulated vessel contains an ideal gas of molecular mass {tex} M {/tex} and ratio of specific heats {tex} \gamma {/tex} . It is moving with speed {tex} v {/tex} and it suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by

A

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

B

{tex} \frac { \gamma M v ^ { 2 } } { 2 R } K {/tex}

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

D

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

##### Explanation

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Q 5. Figure shows a parabolic graph between {tex} \mathrm { T } {/tex} and {tex}1 / \mathrm { V } {/tex} for a mixture of a gases undergoing an adiabatic process. What is the ratio of {tex} \mathrm { V } _ { \mathrm { ms } } {/tex} of molecules and speed of sound in mixture?

A

{tex} \sqrt { 3 / 2 } {/tex}

{tex} \sqrt { 2 } {/tex}

C

{tex} \sqrt { 2 / 3 } {/tex}

D

{tex} \sqrt { 3 } {/tex}

##### Explanation

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Q 6. The work of 146{tex} \mathrm { kJ } {/tex} is performed in order to compress one kilomole of gas adiabatically and in this process the temperature of the gas increases by {tex} 7 ^ { \circ } \mathrm { C } {/tex} . The gas is {tex} \left( R = 8.3 \mathrm { J } \mathrm { mol } ^ { - 1 } \mathrm { K } ^ { - 1 } \right) {/tex}

diatomic

B

triatomic

C

a mixture of monatomic and diatomic

##### Explanation

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Q 7. At what temperature is root mean square velocity of gaseous hydrogen molecules equal to that of oxygen molecules at {tex} 47 ^ { \circ } \mathrm { C } ? {/tex}

A

{tex}40 \mathrm { K } {/tex}

B

{tex}80 \mathrm { K } {/tex}

C

{tex} - 73 K {/tex}

{tex}20 \mathrm { K } {/tex}

##### Explanation

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Q 8. The kinetic theory of gases states that the average squared velocity of molecules varies linearly with the mean molecular weight of the gas. If the root mean square (rms) velocity of oxygen molecules at a certain temperature is 0.5{tex} \mathrm { km } / \mathrm { sec } {/tex} . The rms velocity for hydrogen molecules at the same temperature will be:

2{tex} \mathrm { km } / \mathrm { sec } {/tex}

B

4{tex} \mathrm { km } / \mathrm { sec } {/tex}

C

8{tex} \mathrm { km } / \mathrm { sec } {/tex}

D

16{tex} \mathrm { km } / \mathrm { sec } {/tex}

##### Explanation

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Q 9. If 2 moles of an ideal monatomic gas at temperature {tex} \mathrm { T } _ { 0 } {/tex} is mixed with 4 moles of another ideal monatomic gas at temperature 2{tex} \mathrm { T } _ { 0 } {/tex} , then the temperature of the mixture is

{tex} \frac { 5 } { 3 } \mathrm { T } _ { 0 } {/tex}

B

{tex} \frac { 3 } { 2 } \mathrm { T } _ { 0 } {/tex}

C

{tex} \frac { 4 } { 3 } \mathrm { T } _ { 0 } {/tex}

D

{tex} \frac { 5 } { 4 } \mathrm { T } _ { 0 } {/tex}

##### Explanation

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Q 10. From the following statements, concerning ideal gas at any given temperature {tex} T , {/tex} select the incorrect one(s)

The coefficient of volume expansion at constant pressure is same for all ideal gas

B

The average translational kinetic energy per molecule of oxygen gas is 3{tex} K T ( K \text { being Boltzmann constant) } {/tex}

C

In a gaseous mixture, the average translational kinetic energy of the molecules of each component is same

D

The mean free path of molecules increases with decrease in pressure

##### Explanation

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Q 11. The adjoining figure shows graph of pressure and volume of a gas at two tempertures {tex} T _ { 1 } {/tex} and {tex} T _ { 2 } {/tex} . Which of the following
inferences is correct?

A

{tex} \mathrm { T } _ { 1 } > \mathrm { T } _ { 2 } {/tex}

B

{tex} \mathrm { T } _ { 1 } = \mathrm { T } _ { 2 } {/tex}

{tex} \mathrm { T } _ { 1 } < \mathrm { T } _ { 2 } {/tex}

D

None of these

##### Explanation

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Q 12. The molecules of a given mass of gas have a root mean square velocity of 200{tex} \mathrm { m } \mathrm { s } ^ { - 1 } {/tex} at {tex} 27 ^ { \circ } \mathrm { C } {/tex} and {tex} 1.0 \times 10 ^ { 5 } \mathrm { N } \mathrm { m } ^ { - 2 } {/tex} pressure. When the temperature is {tex} 127 ^ { \circ } \mathrm { C } {/tex} and the pressure {tex} 0.5 \times 10 ^ { 5 } \mathrm { Nm } ^ { - 2 } {/tex} , the root mean square velocity in {tex} \mathrm { ms } ^ { - 1 } , {/tex} is

{tex} \frac { 400 } { \sqrt { 3 } } {/tex}

B

100{tex} \sqrt { 2 } {/tex}

C

{tex} \frac { 100 \sqrt { 2 } } { 3 } {/tex}

D

{tex} \frac { 100 } { 3 } {/tex}

##### Explanation

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Q 13. A graph is plotted with PV/T on y-axis and mass of the gas along {tex} x {/tex} -axis for different gases. The graph is

A

a straight line parallel to {tex} x {/tex} -axis for all the gases

B

a straight line passing through origin

a straight line passing through origin with a slope having different values for different gases

D

a straight line parallel to y-axis for all the gases

##### Explanation

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Q 14. At identical temperatures, the rms speed of hydrogen molecules is 4 times that for oxygen molecules. In a mixture of these in mass ratio {tex} \mathrm { H } _ { 2 } : \mathrm { O } _ { 2 } = 1.8 , {/tex} the rms speed of all molecules is n times the rms speed for {tex} \mathrm { O } _ { 2 } {/tex} , molecules, where {tex} \mathrm { n } {/tex} is

A

3

B

4/3

C

{tex} ( 8 / 3 ) ^ { 1 / 2 } {/tex}

{tex} ( 11 ) ^ { 1 / 2 } {/tex}

##### Explanation

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Q 15. Work done by a system under isothermal change from a volume {tex} \mathrm { V } _ { 1 } {/tex} to {tex} \mathrm { V } _ { 2 } {/tex} for a gases which obeys Vander Waal's equation {tex} ( V - \beta n ) \left( P + \frac { \alpha n ^ { 2 } } { V } \right) = n R T {/tex} is

{tex} n R T \log _ { e } \left( \frac { V _ { 2 } - n \beta } { V _ { 1 } - n \beta } \right) + \alpha n ^ { 2 } \left( \frac { V _ { 1 } - V _ { 2 } } { V _ { 1 } V _ { 2 } } \right) {/tex}

B

{tex} n R T \log _ { 10 } \left( \frac { V _ { 2 } - n \beta } { V _ { 1 } - n \beta } \right) + \alpha n ^ { 2 } \left( \frac { V _ { 1 } - V _ { 2 } } { V _ { 1 } V _ { 2 } } \right) {/tex}

C

{tex} n R T \log _ { e } \left( \frac { V _ { 2 } - n \beta } { V _ { 1 } - n \beta } \right) + \beta n ^ { 2 } \left( \frac { V _ { 1 } - V _ { 2 } } { V _ { 1 } V _ { 2 } } \right) {/tex}

D

{tex} n R T \log _ { e } \left( \frac { V _ { 1 } - n \beta } { V _ { 2 } - n \beta } \right) + \alpha n ^ { 2 } \left( \frac { V _ { 1 } V _ { 2 } } { V _ { 1 } - V _ { 2 } } \right) {/tex}

##### Explanation

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Q 16. The temperature of the mixture of one mole of helium and one mole of hydrogen is increased from {tex} 0 ^ { \circ } \mathrm { C } {/tex} to {tex} 100 ^ { \circ } \mathrm { C } {/tex} at constant pressure. The amount of heat delivered will be

A

600{tex} \mathrm { cal } {/tex}

1200{tex} \mathrm { cal } {/tex}

C

1800{tex} \mathrm { cal } {/tex}

D

3600{tex} \mathrm { cal } {/tex}

##### Explanation

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Q 17. If the intermolecular forces vanish away, the volume occupied by the molecules contained in 4.5{tex} \mathrm { g } {/tex} water at standard temperature and pressure will be

5.6 litre

B

4.5 litre

C

11.2 litre

D

6.5 litre

##### Explanation

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Q 18. A gas mixture consists of 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

{tex}4 \mathrm{RT}{/tex}

B

{tex} 15 \mathrm { RT } {/tex}

C

{tex}9 \mathrm { RT } {/tex}

{tex} 11\mathrm { RT } {/tex}

##### Explanation

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Q 19. For a gas, if ratio of specific heats at constant pressure and volume is {tex} \gamma {/tex} then value of degrees of freedom is

A

{tex} \frac { 3 \gamma - 1 } { 2 \gamma - 1 } {/tex}

{tex} \frac { 2 } { \gamma - 1 } {/tex}

C

{tex} \frac { 9 } { 2 } ( \gamma - 1 ) {/tex}

D

{tex} \frac { 25 } { 2 } ( \gamma - 1 ) {/tex}

##### Explanation

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Q 20. The given {tex} P - V {/tex} curve is predicted by

Boyle's law

B

Charle's law

C

D

Gaylussac's law

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Q 21. Three perfect gases at absolute temperatures {tex} T _ { 1 } , T _ { 2 } {/tex} and {tex} T _ { 3 } {/tex} are mixed. The masses of molecules are {tex} m _ { 1 } , m _ { 2 } {/tex} and {tex} m _ { 3 } {/tex} and the number of molecules are {tex} n _ { 1 } , n _ { 2 } {/tex} and {tex} n _ { 3 } {/tex} respectively. Assuming no loss of energy, the final temperature of the mixture is:

{tex} \frac { n _ { 1 } T _ { 1 } + n _ { 2 } T _ { 2 } + n _ { 3 } T _ { 3 } } { n _ { 1 } + n _ { 2 } + n _ { 3 } } {/tex}

B

{tex} \frac { n _ { 1 } T _ { 1 } ^ { 2 } + n _ { 2 } T _ { 2 } ^ { 2 } + n _ { 3 } T _ { 3 } ^ { 2 } } { n _ { 1 } T _ { 1 } + n _ { 2 } T _ { 2 } + n _ { 3 } T _ { 3 } } {/tex}

C

{tex} \frac { n _ { 1 } ^ { 2 } T _ { 1 } ^ { 2 } + n _ { 2 } ^ { 2 } T _ { 2 } ^ { 2 } + n _ { 3 } ^ { 2 } T _ { 3 } ^ { 2 } } { n _ { 1 } T _ { 1 } + n _ { 2 } T _ { 2 } + n _ { 3 } T _ { 3 } } {/tex}

D

{tex} \frac { \left( T _ { 1 } + T _ { 2 } + T _ { 3 } \right) } { 3 } {/tex}

##### Explanation

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Q 22. A gas is enclosed in a cube of side {tex} l . {/tex} What will be the change in momentum of the molecule, if it suffers an elastic collision with the plane wall parallel to {tex} y z {/tex} -plane and rebounds with the same velocity? {tex} \left[ \left( V _ { x } , V _ { y } \& V _ { z } \right) \text { initial velocities of the gas molecules } \right] {/tex}

A

{tex} m v _ { x } {/tex}

B

zero

C

{tex}-mx_{x}{/tex}

{tex} - 2 m v _ { x } {/tex}

##### Explanation

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Q 23. What will be the ratio of number of molecules of a monoatomic and a diatomic gas in a vessel, if the ratio of their partial pressures is 5:3?

A

{tex} 5 : 1 {/tex}

B

{tex} 3 : 1 {/tex}

{tex} 5 : 3 {/tex}

D

{tex} 3 : 5 {/tex}

##### Explanation

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Q 24. Consider a gas with density {tex} \rho {/tex} and {tex} \overline { c } {/tex} as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity {tex} v , {/tex} then the pressure exerted by the gas is

{tex} \frac { 1 } { 3 }\rho \overline { c } ^ { 2 } {/tex}

B

{tex} \frac { 1 } { 3 } \rho ( c + v ) ^ { 2 } {/tex}

C

{tex} \frac { 1 } { 3 } \rho ( \overline { c } - v ) ^ { 2 } {/tex}

D

{tex} \frac { 1 } { 3 } \rho \left( c ^ { - 2 } - v \right) ^ { 2 } {/tex}

##### Explanation

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Q 25. For a gas, difference between two specific heats is 5000{tex} \mathrm { J } / {/tex} mole {tex} ^ { \circ } \mathrm { C } {/tex} . If the ratio of specific heats is {tex} 1.6 , {/tex} the two specific heats in {tex} \mathrm { J } / \mathrm { mole } - ^ { \circ } \mathrm { C } {/tex} are

A

{tex} C _ { P } = 1.33 \times 10 ^ { 4 } , C _ { v } = 2.66 \times 10 ^ { 4 } {/tex}

B

{tex} \mathrm { C } _ { \mathrm { p } } = 13.3 \times 10 ^ { 4 } , \mathrm { C } _ { \mathrm { y } } = 8.33 \times 10 ^ { 3 } {/tex}

{tex} C _ { P } = 1.33 \times 10 ^ { 4 } , C _ { y } = 8.33 \times 10 ^ { 3 } {/tex}

D

{tex} C _ { P } = 2.6 \times 10 ^ { 4 } , C _ { v } = 8.33 \times 10 ^ { 4 } {/tex}