The van der Waals equation of state can be written as P $=$k$\_$B T $\backslash$rho $/(1-$ b$\backslash$rho $)-$a$\backslash$rho $^2,$ where $\backslash$rho $=$ N$/$V and a and b are positive constants.

$($a$)$ Find the change in molar internal energy, $\backslash$Delta e$,$ upon isothermal expansion of such a fluid from molar volume v$1$ to v$2.$

$($b$)$ Is this change greater or less than that for an adiabatic expansion between the same two volumes?