Kinetic Theory of Gases and ldeal Gas | Physics JEE previous year questions with Solutions

Q 11 :

The given figure represents two isobaric processes for the same mass of an ideal gas, then [2024]

$P_{1} > P_{2}$
$P_{2} > P_{1}$
$P_{1} = P_{2}$
$P_{2} < P_{1}$

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(1)

$P V = n R T \Rightarrow V = (\frac{n R}{P}) T$

$Slope = \frac{n R}{P} \Rightarrow Slope \propto \frac{1}{P}$

${(Slope)}_{2} > {(Slope)}_{1} \Rightarrow P_{2} < P_{1}$

Q 12 :

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature? [2025]

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(1)

Mean squared velocity $= {(v_{ms})}^{2} = \frac{3 R T}{M}$ i.e., (mean squared velocity) $\propto$ (Temperature). Hence, graph is a straight line.

Q 13 :

The ratio of vapour densities of two gases at the same temperature is $\frac{4}{25}$ , then the ratio of r.m.s. velocities will be: [2025]

$\frac{25}{4}$
$\frac{2}{5}$
$\frac{5}{2}$
$\frac{4}{25}$

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(3)

$v_{rms} = \sqrt{\frac{3 R T}{M}}$

$\frac{v_{1}}{v_{2}} = \sqrt{\frac{M_{2}}{M_{1}}} = \sqrt{\frac{25}{4}} = \frac{5}{2}$

Q 14 :

Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4% when heated by 1°C. Its initial temperature must be: [2025]

25°C
2500 K
250 K
250°C

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(3)

Isochoric process, P $\propto$ T

$\frac{P}{T} = constant \Rightarrow \frac{△ P}{P} = \frac{△ T}{T}$

$\frac{0.4}{100} = \frac{1}{T} \Rightarrow T = \frac{100}{0.4} = 250 K$

Q 15 :

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $3 \times 10^{- 7} m$ and 600 m/s, respectively. Find the frequency of its collisions. [2025]

$2 \times 10^{10} / s$
$9 \times 10^{5} / s$
$2 \times 10^{9} / s$
$5 \times 10^{2} / s$

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(3)

Frequency of collision $= \frac{average speed}{mean free path}$

$= \frac{600}{3 \times 10^{- 7}} = 2 \times 10^{9} / s$

Q 16 :

There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K, at steady state the pressure in the vessels will be (in kPa). [2025]

4.4
6
24
18

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(2)

Number of masses will remain constant

$n_{1} + n_{2} = n_{f}$

$\frac{P_{1} V_{1}}{R T_{1}} + \frac{P_{2} V_{2}}{R T_{2}} = \frac{P_{f} V_{f}}{R T_{f}}$

$\frac{8 \times 2 V}{R \times 1000} + \frac{7 \times V}{R \times 500} = \frac{P_{f} (3 V)}{R \times 600}$

$\frac{16}{1000} + \frac{14}{1000} = \frac{P_{f}}{200}$

$\frac{30}{1000} = \frac{P_{f}}{200} \Rightarrow P_{f} = 6 kPa$

Q 17 :

A container of fixed volume contains a gas at 27°C. To double the pressure of the gas, the temperature of gas should be raised to ________ °C. [2025]

0%

(327)

For V = constant, $\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}$

$\frac{P}{300} = \frac{2 P}{T_{2}}$

$T_{2} = 600 K = 327 ° C$

Q 18 :

Given below are two statements: [2023]

Statement I: The temperature of a gas is −73°C. When the gas is heated to 527°C, the root mean square speed of the molecules is doubled.

Statement II: The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.

In the light of the above statements, choose the correct answer from the options given below:

Statement I is false but Statement II is true
Both Statement I and Statement II are true
Both Statement I and Statement II are false
Statement I is true but Statement II is false

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(4)

$Statement-I$

$T_{1} = - 73 ° C = 200 K$

$T_{2} = 527 ° C = 800 K$

$\frac{V_{1}}{V_{2}} = \frac{\sqrt{\frac{3 R T_{1}}{M}}}{\sqrt{\frac{3 R T_{2}}{M}}} = \sqrt{\frac{T_{1}}{T_{2}}} = \sqrt{\frac{200}{800}} = \frac{1}{2}$

$V_{2} = 2 V_{1} (True)$

$Statement-II$

$KE = \frac{3}{2} P V$

Q 19 :

The root mean square velocity of molecules of gas is [2023]

inversely proportional to square root of temperature $\sqrt{\frac{1}{T}}$
proportional to square root of temperature $\sqrt{T}$
proportional to square of temperature $T^{2}$
proportional to temperature $T$

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(2)

$V_{rms} = \sqrt{\frac{3 R T}{M}}$

$so$ $V_{rms} \propto \sqrt{T}$

Q 20 :

A bicycle tyre is filled with air having pressure of 270 kPa at 27°C. The approximate pressure of the air in the tyre when the temperature increases to 36°C is [2023]

270 kPa
262 kPa
278 kPa
360 kPa

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(3)

$Taking volume constant: \frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}$

$\Rightarrow P_{2} = \frac{P_{1}}{T_{1}} \times T_{2} = \frac{270 \times 309}{300} = 278 kPa$

Topic Question Set

Q 11 :

The given figure represents two isobaric processes for the same mass of an ideal gas, then [2024]

Q 12 :

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature? [2025]

Q 13 :

The ratio of vapour densities of two gases at the same temperature is $\frac{4}{25}$ , then the ratio of r.m.s. velocities will be: [2025]

Q 14 :

Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4% when heated by 1°C. Its initial temperature must be: [2025]

Q 15 :

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $3 \times 10^{- 7} m$ and 600 m/s, respectively. Find the frequency of its collisions. [2025]

Q 17 :

A container of fixed volume contains a gas at 27°C. To double the pressure of the gas, the temperature of gas should be raised to ________ °C. [2025]

0%

Q 19 :

The root mean square velocity of molecules of gas is [2023]

Q 20 :

A bicycle tyre is filled with air having pressure of 270 kPa at 27°C. The approximate pressure of the air in the tyre when the temperature increases to 36°C is [2023]

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