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) $\infty$ (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 $\infty$ 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, $\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}$

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

$T_{2} = 600 K = 327 ° C$

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%

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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 425, 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 3×10–7 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]

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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]