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  4. A mass of an ideal gas undergoes a reversible isothermal compression. Its molecules will then have compared with initial state, the same (i) root mean square velocity (ii) mean momentum (iii) mean kinetic energy

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Q. A mass of an ideal gas undergoes a reversible isothermal compression. Its molecules will then have compared with initial state, the same
(i) root mean square velocity
(ii) mean momentum
(iii) mean kinetic energy

Thermodynamics

Solution:

Isothermal compression $\Rightarrow T=$ constant
$v_{ rms }=\sqrt{\frac{3 R T}{M}}$
Mean momentum $=m \bar{v}=m \cdot \sqrt{\frac{8 R T}{\pi M}}$
Mean kinetic energy $=\frac{3}{2} R T$
All the above are functions of temperature, which is a constant.