Free expansion are adiabatic expansions and there is no exchange of heat between a system and its environment.

There is no work done on the system or by the system.

It is an instantaneous change, and the system is not in thermodynamic equilibrium

A free expansion can be plotted on a p-v diagram.

900 R

$\quad 300 \mathrm{R}$

1200 R

600 R

473 K

373.25 K

293.29 K

268.25 K

$\mathrm{VT}^2=$ constant

$\frac{\mathrm{V}}{\mathrm{T}^2}=$ constant

$\frac{\mathrm{V}^2}{\mathrm{~T}}=$ constant

$\mathrm{V}^2 \cdot \mathrm{~T}=$ constant