Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 18 - Exercises and Problems: 50

Answer

The proof is below.

Work Step by Step

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.
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