Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 14: Partial Derivatives - Practice Exercises - Page 864: 23


$P_n=\frac{RT}{V}$ $P_R=\frac{nT}{V}$ $P_T=\frac{nR}{V}$ $P_V=\frac{-nRT}{V^2}$

Work Step by Step

Take the first partial derivatives of the given function. When taking partial derivative with respect to n, treat R, T, and V as constants. Use the same method when taking partial derivative with respect to R, T, and V: $P_n=\frac{1RT}{V}=\frac{RT}{V}$ $P_R=\frac{n1T}{V}=\frac{nT}{V}$ $P_T=\frac{nR1}{V}=\frac{nR}{V}$ $P_V=\frac{-nRT}{V^2}$
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