University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 13 - Practice Exercises - Page 749: 23

Answer

$\dfrac{RT}{V}, \dfrac{nT}{V},\dfrac{nR}{V}, -\dfrac{nRT}{V^2}$

Work Step by Step

Given: $P=\dfrac{nRT}{V}$ Now, $\dfrac{\partial P}{\partial n}=\dfrac{\partial }{\partial n} [\dfrac{nRT}{V}]=\dfrac{RT}{V}$ and $\dfrac{\partial P}{\partial R}=\dfrac{\partial }{\partial R} [\dfrac{nRT}{V}]=\dfrac{nT}{V}$ and $\dfrac{\partial P}{\partial T}=\dfrac{\partial }{\partial T} [\dfrac{nRT}{V}]=\dfrac{nR}{V}$ and $\dfrac{\partial P}{\partial V}=\dfrac{\partial }{\partial V} [\dfrac{nRT}{V}]=-\dfrac{nRT}{V^2}$ Hence, $\dfrac{RT}{V}, \dfrac{nT}{V},\dfrac{nR}{V}, -\dfrac{nRT}{V^2}$
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