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If a gas is compressed isothermally then the r.m.s. velocity of the molecules
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The correct answer is:
remains the same.
The root-mean-square (rms) velocity of gas molecules is,
$$
\mathrm{v}_{\mathrm{r} . \mathrm{m} . \mathrm{s}}=\sqrt{\frac{3 \mathrm{kT}}{\mathrm{m}}}
$$
$\Rightarrow \mathrm{v}_{\mathrm{rms}} \propto \sqrt{\mathrm{T}}$ for a given gas.
As the temperature is constant in isothermal process, the r.m.s velocity remains the same.
$$
\mathrm{v}_{\mathrm{r} . \mathrm{m} . \mathrm{s}}=\sqrt{\frac{3 \mathrm{kT}}{\mathrm{m}}}
$$
$\Rightarrow \mathrm{v}_{\mathrm{rms}} \propto \sqrt{\mathrm{T}}$ for a given gas.
As the temperature is constant in isothermal process, the r.m.s velocity remains the same.
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