Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 14 - The Ideal Gas Law and Kinetic Theory - Problems - Page 387: 64

Answer

1983.13 N/m

Work Step by Step

Let's take, The cross-sectional area of the piston = A Length of the cylinder = L The volume of the cylinder = V According to Boyle's law, we can write, $P_{1}V_{1}=P_{2}V_{2}=>P_{2}=\frac{P_{1}V_{1}}{V_{2}}=P_{1}(\frac{AL_{1}}{AL_{2}})=P_{1}(\frac{L_{1}}{L_{2}})$ Let's plug known values into this equation. $P_{2}=(1.01\times10^{5}Pa)(\frac{L}{2L})=5.05\times10^{4}Pa$ The force on the piston = $P_{2}A=kx$ and spring (F) $k=\frac{P_{2}A}{x}=\frac{(5.05\times10^{4}Pa)\pi(0.05\space m)^{2}}{0.2\space m}=1983.13\space N/m$ Spring constant = 1983.13 N/m
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