Vardaan Learning Institute

Derive the pressure exerted by an ideal gas $P = \frac{1}{3} n m v_{rms}^2$ starting from elastic collision of gas molecules with a container wall.

A vertical cylinder closed at both ends is divided into two equal halves by a frictionless piston of mass $m$. Each half contains 1 mole of air at temperature $T_0$. If cylinder is turned upside down, find final temperature $T$ required to restore piston to middle position.