MHT CET · Physics · Kinetic Theory of Gases
If a gas is compressed isothermally then the r.m.s. velocity of the molecules
- A decreases.
- B increases.
- C remains the same.
- D first decreases and then increases.
Answer & Solution
Correct Answer
(C) remains the same.
Step-by-step Solution
Detailed explanation
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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