If a gas is compressed isothermally then the r.m.s. velocity of the molecules

If a gas is compressed isothermally then the r.m.s. velocity of the molecules
  1. remains the same.
  2. increases.
  3. decreases.
  4. first decreases and then increases.

Solution

Root mean square (r.m.s) velocity of the molecules $\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}$ $\Rightarrow \mathrm{v}_{\mathrm{rms}} \propto \sqrt{\mathrm{~T}}$ But in isothermal process, temperature remains constant. Thus the r.m.s velocity of the molecules remains constant.

Asked in: MHT CET 2020 (15 Oct Shift 2)

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