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

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.