Case $-1:$ An ideal gas of molecular weight $M$ at temperature $T$. Case $-2:$ Another ideal gas of molecular weight $2 \mathrm{M}$ at temperature $\mathrm{T} / 2$ Identify the correct statement in context of above two cases.

Question

Case $-1:$ An ideal gas of molecular weight $M$ at temperature $T$. Case $-2:$ Another ideal gas of molecular weight $2 \mathrm{M}$ at temperature $\mathrm{T} / 2$ Identify the correct statement in context of above two cases., Average kinetic energy and avereage speed will be the same in the two cases, Both the averages are halved, Both the averages are doubled, Only average speed is halved in the second case

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Hint : As temperature is halved, average $K E$ is halved. Average speed $(C) \propto \sqrt{\frac{T}{M}}$ In case $-I,(C) \propto \sqrt{\frac{T}{M}}$ $\text { In case }-II ~(C) \propto \sqrt{\frac{T}{2 \times 2 M}}=\frac{1}{2} \sqrt{\frac{T}{M}}$ So average speed is also halved.

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