(B) For an ideal gas,the translational kinetic energy $K$ is given by $K = \frac{3}{2} PV$. Thus,$PV = \frac{2}{3} K$. Options $A$ and $D$ are incorre

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The temperature of a gas is $-73^{\circ} C$. When the gas is heated to $527^{\circ} C$,the r.m.s. speed of the molecules is doubled.

(B) For an ideal gas,the translational kinetic energy $K$ is given by $K = \frac{3}{2} PV$. Thus,$PV = \frac{2}{3} K$. Options $A$ and $D$ are incorrect.For r.m.s. speed,$v_{rms} \propto \sqrt{T}$.In option $B$: $T_1 = -73 + 273 = 200 \ K$ and $T_2 = 527 + 273 = 800 \ K$. The ratio $\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{800}{200}} = \sqrt{4} = 2$. Thus,the r.m.s. speed doubles. Option $B$ is correct.In option $C$: $T_1 = -100 + 273 = 173 \ K$ and $T_2 = 627 + 273 = 900 \ K$. The ratio $\frac{v_2}{v_1} = \sqrt{\frac{900}{173}} \neq 4$. Option $C$ is incorrect.

Class 11 Physics Kinetic Theory of Gases Mix Examples-Kinetic Theory of Gases

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A
The product of pressure and volume of an ideal gas is equal to the translational kinetic energy of the molecules.
B
The temperature of a gas is $-73^{\circ} C$. When the gas is heated to $527^{\circ} C$,the r.m.s. speed of the molecules is doubled.
C
The temperature of a gas is $-100^{\circ} C$. When the gas is heated to $+627^{\circ} C$,the r.m.s. speed of the molecules is four times.
D
The product of pressure and volume of an ideal gas is equal to half the translational kinetic energy.

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Mix Examples-Kinetic Theory of Gases

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An ideal gas of molar mass $M$ is contained in a very tall vertical cylindrical column in a uniform gravitational field. Assuming the gas temperature to be $T$, the height at which the centre of gravity of the gas is located is (where $R$ is the universal gas constant).

If the potential energy of a gas molecule is $U = \frac{M}{r^6} - \frac{N}{r^{12}}$,where $M$ and $N$ are positive constants,then the potential energy at equilibrium must be

If a closed container containing gas is in motion and is suddenly stopped,the random motion of the gas molecules will .......

The average translational kinetic energy of $N$ molecules in a gas is $E_1$. The kinetic energy of the electron $(e)$ accelerated from rest through potential difference $V$ volt is $E_2$. The temperature at which $E_1=E_2$ is possible is ( $R=$ gas constant,$N=$ number of molecules).

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