Select the correct statement.

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(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.

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(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 $\frac{v_2}{v_1} = \sqrt{\frac{900}{173}} 
eq 4$. Option $C$ is incorrect.

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