Answer
Please see the work below.
Work Step by Step
We know that in adiabatic process
$PV^{\gamma}=constant$......eq(1)
For ideal gas
$PV=nRT$
This can be rearranged as:
$V=\frac{nRT}{P}$......eq(2)
We plug in the value of V from equation(2) into equation(1)
$P(\frac{nRT}{P})^{\gamma}=constant$
This can be rearranged as:
$P^{1-\gamma}T^{\gamma}=\frac{constant}{(nR)^{\gamma}}=constant$ (because nR is constant)
