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: 69

Answer

The proof is below.

Work Step by Step

We know that equation 18.3 states: $W=-\int_{V_1}^{V_2}PdV$ For an adiabatic process, we know the following equation is true: $PV^{\gamma}=c$ Where c is a constant. Substituting this equation into equation 18.3 and taking the integral, it follows: $W = P(\frac{V_2-V_1}{\gamma-1})$ $W = (\frac{PV_2-PV_1}{\gamma-1})$ This is equation 18.12.
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