Answer
The proof is below.
Work Step by Step
We know the following:
$P_1V_1^{\gamma} = P_2V_2^{\gamma} $
We use the ideal gas law to find:
$p_1=\frac{RT_1}{V_1}$
$p_2=\frac{RT_2}{V_2}$
Combining these three equations gives:
$\frac{RT_1}{V_1}V_1^{\gamma} =\frac{RT_2}{V_2}V_2^{\gamma} $
$T_1V_1^{\gamma-1}=T_2V_2^{\gamma-1} $
$T_1V_1^{\gamma-1}=k$
Where k is a constant.
