The temperature of a gas is doubled (i) on th | vedclass

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(A) The root mean square velocity of a gas is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $T$ is the absolute temperature.Case $(i)$: The absolute

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More in case $(i)$

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(A) The root mean square velocity of a gas is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $T$ is the absolute temperature.Case $(i)$: The absolute temperature $T$ is doubled,so $T' = 2T$. The new velocity is $v'_{rms} = \sqrt{\frac{3R(2T)}{M}} = \sqrt{2} v_{rms} \approx 1.414 v_{rms}$.Case $(ii)$: The centigrade temperature $t$ is doubled,so $t' = 2t$. The absolute temperature becomes $T' = (2t + 273) = 2(T - 273) + 273 = 2T - 273$. Since $2T - 273 Since $v_{rms} \propto \sqrt{T}$,the increase in velocity is greater when the absolute temperature is doubled compared to when the centigrade temperature is doubled. Therefore,the increase is more in case $(i)$.

The temperature of a gas is doubled $(i)$ on the absolute scale and $(ii)$ on the centigrade scale. The increase in the root mean square velocity of the gas will be:

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