#### Answer

The new temperature of the gas is $1.5~T_0$.

#### Work Step by Step

We can find an expression for the initial temperature as:
$P_1V_1 = nRT_0$
$T_0 = \frac{P_1V_1}{nR}$
We can find the new temperature.
$P_2V_2 = nRT_2$
$T_2 = \frac{P_2V_2}{nR}$
$T_2 = \frac{(P_1/2)(3V_1)}{nR}$
$T_2 = 1.5~\frac{P_1V_1}{nR}$
$T_2 = 1.5~T_0$
The new temperature of the gas is $1.5~T_0$.