Problem-TH-04002

The molar energy of a monoatomic gas which obeys van der Waal's equation is given by
\( E= \frac{3}{2}kT - \frac{a}{v}\),
where \(V\) is the volume at temperature \(T\), and \(a\) is a constant. Initially one mole of gas is at temperature \(T_1\) and occupies volume \(V_1\). The gas is allowed to  expand adiabatically into a vacuum so that it occpies a total volume \(V_2\). What is the final temperature of the gas?

MANDL