Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - 14.5 The Chain Rule - 14.5 Exercises - Page 985: 41

Answer

$$\approx -0.27 L/s$$

Work Step by Step

We need to apply chain rule as follows: $$\dfrac{dV}{dt}=(\dfrac{\partial V}{\partial P})(\dfrac{dP}{ dt})+(\dfrac{\partial V}{\partial T})(\dfrac{dT}{dt})\\ =(-8.31) \times \dfrac{T}{P^2} \times \dfrac{dP}{ dt} +8.31 \times (\dfrac{1}{P}) \times \dfrac{dT}{dt} \\=(-8.31) \times [-\dfrac{320}{(20)^2}] (0.05)+(\dfrac{1}{ 20}) \times (0.15)] \\ \approx -0.27 L/s$$
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