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

For an isothermal process, the following is true: $PV=c$ Where c is an arbitrary constant. Thus, we find: $\frac{dP}{dV}=-\frac{p}{V}$ For an adiabatic process, the following is true: $PV^{\gamma}=c$ Where c is an arbitrary constant. Thus, we find: $\frac{dP}{dV}=-\gamma \frac{P}{V}$ Thus, the proof is complete.