Pho.rs: Oscillating piston

Условие

T Условие

PC25

Русский

A monoatomic gas fills a cylinder of height $H$ under a piston. The piston oscillates periodically up and down with amplitude $a$: during the first half-period, it moves upward with a constant speed $u$, and during the second half-period, it moves downward with the same constant speed $u$. Initially, the root-mean-square (RMS) speed of the molecules is $v$.

How much time $t$ will it take for the RMS speed to double?

Use the following model assumptions: the walls and the piston are perfect heat insulators and have zero heat capacity; the surface of the piston is perfectly flat; the mean free path of the molecules $\lambda$ satisfies the following conditions: $H \gg \lambda \gg a$ and $\lambda \gg H^2/(vt)$ ; additionally, $v \gg u$.