By how many folds will the temperature of a g | vedclass

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(D) The root mean square velocity $(V_{rms})$ is given by the formula: $V_{rms} = \sqrt{\frac{3RT}{M}}$.Since $R$ and $M$ are constant,$V_{rms} \propt

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$4$

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(D) The root mean square velocity $(V_{rms})$ is given by the formula: $V_{rms} = \sqrt{\frac{3RT}{M}}$.Since $R$ and $M$ are constant,$V_{rms} \propto \sqrt{T}$,which implies $\frac{V_1}{V_2} = \sqrt{\frac{T_1}{T_2}}$.Given $V_1 = 5 	imes 10^4 \ cm/s$ and $V_2 = 10 	imes 10^4 \ cm/s$,we have $\frac{5 	imes 10^4}{10 	imes 10^4} = \frac{1}{2} = \sqrt{\frac{T_1}{T_2}}$.Squaring both sides,we get $\frac{1}{4} = \frac{T_1}{T_2}$,which means $T_2 = 4T_1$.Therefore,the temperature increases by $4$ folds.

By how many folds will the temperature of a gas increase when the root mean square velocity of the gas molecules in a container of fixed volume is increased from $5 \times 10^4 \ cm/s$ to $10 \times 10^4 \ cm/s$?

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