Essential University Physics: Volume 1 (4th Edition)

Published by Pearson
ISBN 10: 0-134-98855-8
ISBN 13: 978-0-13498-855-9

Chapter 18 - Exercises and Problems - Page 344: 74


The proof is below.

Work Step by Step

When solving for equation 18.4, the book used the following equation: $W = -nRT \int_{V_1}^{V_2}PdV$ We first solve the van der Waals equation for P: $P=\frac{nRT}{v-nb}-a(\frac{n^2}{v^2})$ We plug this into the equation for work: $W = -nRT \int_{V_1}^{V_2}(\frac{nRT}{V-nb}-a(\frac{n^2}{V^2}))dV$ Not surprisingly, when we evaluate this integral, we find: $W = -nRTln(\frac{V_2}{V_1})$ This is the same as equation 18.4.
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