thermodynamics question

Where does Cv= 3/2 R come from??

From the elementary kinetic theory of gases, you can show that the average KE per molecule is $\frac{3}{2}kT$ so that the energy per mole is $U= N_A \times \frac{3}{2}kT = \frac{3}{2}RT$. Then by definition, we have:

$C_V=(\frac{\partial U}{\partial T})_V = \frac{3}{2}R$

So the important bit is working out the energy per molecule. This is a standard derivation though.