In an adiabatic process, R = \(\frac{2}{3}C_V\). The pressure of the gas will be proportional to : 

T^5/2

\(R = \frac{2}{3}C_V\)

We know : C_P - C_V = R

\(\gamma - 1 = \frac{R}{C_v}\)

\(R = C_V(\gamma - 1)\)

Comparing : \(\gamma = \frac{5}{3}\)

P^\(1-\gamma\)T^\(\gamma\) = constant = K

\(P \propto T^{\frac{\gamma}{\gamma - 1}} \text{ ... [given : } \gamma = \frac{5}{3}]\)

\(\frac{\gamma}{\gamma - 1} = \frac{5}{2}\)

\(P \propto T^{5/2}\)