Question

An adiabatic chamber has frictionless insulated piston of mass m. Mass of the remaining chamber including gas is 4m .'n' moles of an ideal monatomic gas is present inside the chamber at atmosphere temperature and pressure. Piston is in rest at equilibrium and confined to move along the length of the cylinder. A particle of mass m moving horizontally with speed v, strikes elastically with the piston. Find the change in temperature of the gas when the compression of the gas is maximum.

Answer 1

Let $T_{atm}$ is the initial temperature of the system.

When particle with velocity $\nu$ strikes to the piston elastically, then velocity acquired by the piston is $\nu$.

So this will be the root mean square velocity of the particles present in the chamber.

$\nu =\sqrt{\frac{3kT}{M}}$

Total molecules are 'n' and total mass is 4m.

Therefore, $\nu$ is given by

$\nu =\sqrt{\frac{3nKT}{4m}}$

$T=\frac{4m{\nu }^2}{3nK}$

So change in pressure = $T-T_{atm}$