Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 14 - Partial Derivatives - 14.5 Exercises - Page 955: 41

Answer

$-0.27 L/s$

Work Step by Step

Apply the chain rule: $\dfrac{dV}{dt}=(\dfrac{\partial V}{\partial P})(\dfrac{dP}{ dt})+(\dfrac{\partial V}{\partial T})(\dfrac{dT}{dt})$ or, $=(-8.31)\dfrac{T}{P^2})(\dfrac{dP}{ dt})+8.31(\dfrac{1}{P})(\dfrac{dT}{dt})$ or, $=(-8.31)[-\dfrac{320}{(20)^2}) \times (0.05)+(\dfrac{1}{ 20})(0.15)]$ or, $ \approx -0.27 L/s$
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