## Essential University Physics: Volume 1 (3rd Edition)

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)