1. Use the adiabatic relation between pressure and density

For an adiabatic process, $P \propto d^{\gamma}$ where $d$ is the density.

So, $\frac{P_2}{P_1}=\left(\frac{d_2}{d_1}\right)^{\gamma}$

Given: $\gamma=\frac{7}{5}, \qquad \frac{d_2}{d_1}=32=2^5$

Hence, $\frac{P_2}{P_1}=32^{7/5}=(2^5)^{7/5}=2^7=128$

2. Use the ideal gas relation

For an ideal gas, $P=\rho R_s T$ where $\rho$ is density. Therefore, $T \propto \frac{P}{d}$

So, $\frac{T_2}{T_1}=\frac{P_2/P_1}{d_2/d_1}$

Substitute the values: $\frac{T_2}{T_1}=\frac{128}{32}=4$

3. Final result

The temperature becomes $4$ times its initial temperature.