NEET > Behaviour of Perfect Gas and Kinetic Theory

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 popular teachers.


Q 1.    

Correct4

Incorrect-1

4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is {tex} 5.0 \mathrm { JK } ^ { - 1 } . {/tex} If the speed of any quantity {tex} \mathrm { x } {/tex} in this gas at NTP is 952{tex} \mathrm { ms } ^ { - 1 } {/tex} , then the heat capacity at constant pressure is (Take gas constant {tex} \left. \mathrm { R } = 8.3 \mathrm { JK } ^ { - 1 } \mathrm { mol } ^ { - 1 } \right) {/tex}

A

7.5{tex} \mathrm { JK } ^ { - 1 } \mathrm { mol } ^ { - 1 } {/tex}

B

7.0{tex} \mathrm { JK } ^ { - 1 } \mathrm { mol } ^ { - 1 } {/tex}

C

8.5{tex} \mathrm { JK } ^ { - 1 } \mathrm { mol } ^ { - 1 } {/tex}

8.0{tex} \mathrm { JK } ^ { - 1 } \mathrm { mol } ^ { - 1 } {/tex}

Explanation

Q 2.    

Correct4

Incorrect-1

A fixed mass of gas at constant pressure occupies a volume V. The gas undergoes a rise in temperature so that the root mean square velocity of its molecules is doubled. The new volume will be

A

{tex} \mathrm { V } / 2 {/tex}

B

{tex} \mathrm { V } / \sqrt { 2 } {/tex}

C

2{tex} \mathrm { V } {/tex}

4{tex} \mathrm { V } {/tex}

Explanation

Q 3.    

Correct4

Incorrect-1

A gaseous mixture consists of 16{tex} \mathrm { g } {/tex} of helium and 16{tex} \mathrm { g } {/tex} of oxygen. The ratio {tex} \frac { C _ { p } } { C _ { y } } {/tex} of the mixture is

1.62

B

1.59

C

1.54

D

1.4

Explanation

Q 4.    

Correct4

Incorrect-1

Air is pumped into an automobile tube upto a pressure of 200{tex} \mathrm { kPa } {/tex} in the morning when the air temperature is {tex} 22 ^ { \circ } \mathrm { C } {/tex} . During the day, temperature rises to {tex} 42 ^ { \circ } \mathrm { C } {/tex} and the tube expands by 2{tex} \% {/tex} . The pressure of the air in the tube at this temperature, will be approximately

A

212{tex} \mathrm { kPa } {/tex}

209{tex} \mathrm { kPa } {/tex}

C

206{tex} \mathrm { kPa } {/tex}

D

200{tex} \mathrm { kPa } {/tex}

Explanation

Q 5.    

Correct4

Incorrect-1

The rms speed of the particles of fume of mass {tex} 5 \times 10 ^ { - 17 } \mathrm { kg } {/tex} executing Brownian motion in air at N.T.P. is {tex} ( \mathrm { k } = 1.38 \times {/tex} {tex} \left. 10 ^ { - 23 } \mathrm { J } / \mathrm { K } \right) {/tex}

A

1.5{tex} \mathrm { m } / \mathrm { s } {/tex}

B

3.0{tex} \mathrm { m } / \mathrm { s } {/tex}

1.5{tex} \mathrm { cm } / \mathrm { s } {/tex}

D

3{tex} \mathrm { cm } / \mathrm { s } {/tex}

Explanation



Q 6.    

Correct4

Incorrect-1

One mole of an ideal monoatomic gas requires 207{tex} \mathrm { J } {/tex} heat to raise the temperature by 10{tex} \mathrm { K } {/tex} when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same {tex} 10 \mathrm { K } , {/tex} the heat {tex} \text { required is [Given the gas constant } \mathrm { R } = 8.3 \mathrm { J } / \mathrm { mol } . \mathrm { K } ] {/tex}

A

198.7{tex} \mathrm { J } {/tex}

B

29{tex} \mathrm { J } {/tex}

C

215.3{tex} \mathrm { J } {/tex}

124{tex} \mathrm { J } {/tex}

Explanation

Q 7.    

Correct4

Incorrect-1

Figure shows the variation in temperature {tex} ( \Delta \mathrm { T } ) {/tex} with the amount of heat supplied {tex} ( \mathrm { Q } ) {/tex} in an isobaric process corresponding to a monoatomic (M), diatomic (D) and a polyatomic (P) gas. The initial state of all the gases are the same and the scales for the two axes coincide. Ignoring vibrational degrees of freedom, the lines {tex} a , b {/tex} and {tex} c {/tex}
respectively correspond to

A

{tex} \mathrm { P } , \mathrm { M } {/tex} and {tex} \mathrm { D } {/tex}

B

{tex} \mathrm { M } , \mathrm { D } {/tex} and {tex} \mathrm { P } {/tex}

{tex} \mathrm { P } , \mathrm { D } {/tex} and {tex} \mathrm { M } {/tex}

D

{tex} \mathrm { D } , \mathrm { M } {/tex} and {tex} \mathrm { P } {/tex}

Explanation

Q 8.    

Correct4

Incorrect-1

1 mole of a monatomic and 2 mole of a diatomic gas are mixed. The resulting gas is taken through a process in which molar heat capacity was found 3{tex} \mathrm { R } {/tex} . Polytropic constant in the process is

{tex} - 1 / 5 {/tex}

B

1{tex} / 5 {/tex}

C

2{tex} / 5 {/tex}

D

{tex} - 2 / 5 {/tex}

Explanation

Q 9.    

Correct4

Incorrect-1

The density of a gas is {tex} 6 \times 10 ^ { - 2 } \mathrm { kg } / \mathrm { m } ^ { 3 } {/tex} and the root mean square velocity of the gas molecules is 500{tex} \mathrm { m } / \mathrm { s } {/tex} . The pressure exerted by the gas on the walls of the vessel is

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

B

{tex} 1.2 \times 10 ^ { - 4 } \mathrm { N } / \mathrm { m } ^ { 2 } {/tex}

C

{tex} 0.83 \times 10 ^ { - 4 } \mathrm { N } / \mathrm { m } ^ { 2 } {/tex}

D

{tex}30 \ \mathrm { N } / \mathrm { m } ^ { 2 } {/tex}

Explanation

Q 10.    

Correct4

Incorrect-1

The absolute temperature of a gas is increases 3 times. The root mean square velocity of the moelcules will be

A

3 times

B

9 times

C

1{tex} / 3 {/tex} times

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

Explanation



Q 11.    

Correct4

Incorrect-1

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

Q 12.    

Correct4

Incorrect-1

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

Q 13.    

Correct4

Incorrect-1

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

Q 14.    

Correct4

Incorrect-1

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

Q 15.    

Correct4

Incorrect-1

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

Q 16.    

Correct4

Incorrect-1

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}

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

B

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

C

{tex} - 73 K {/tex}

D

3{tex} \mathrm { K } {/tex}

Explanation

Q 17.    

Correct4

Incorrect-1

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


Q 18.    

Correct4

Incorrect-1

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

Q 19.    

Correct4

Incorrect-1

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

A

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

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

Q 20.    

Correct4

Incorrect-1

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

Q 21.    

Correct4

Incorrect-1

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

Q 22.    

Correct4

Incorrect-1

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 with a slope having different values for different gases

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

Q 23.    

Correct4

Incorrect-1

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

Q 24.    

Correct4

Incorrect-1

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



Q 25.    

Correct4

Incorrect-1

Two vessels separately contain two ideal gases {tex} A {/tex} and {tex} B {/tex} at the same temperature. The pressure of A being twice that of B. Under such conditions, the density of {tex} A {/tex} is found to be 1.5 times the density of {tex} B {/tex} . The ratio of molecular weight of {tex} A {/tex} and {tex} B {/tex} is:

{tex} \frac { 3 } { 4 } {/tex}

B

2

C

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

D

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

Explanation