Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 17 - Exercises and Problems - Page 315: 75


The proofs are below.

Work Step by Step

a) Equation 14.9 states: $ v =\sqrt{\frac{\gamma P}{\rho}}$ The ideal gas law states: $ P =\frac{nRT}{V}$ Thus: $ v =\sqrt{\frac{\gamma \frac{nRT}{V}}{\rho}}$ Finally, we know that $\rho=\frac{m}{V}$. Thus: $ v =\sqrt{\frac{\gamma nRT}{m}}$ Therefore, we find: $v_{sound} =\sqrt{\frac{\gamma kT}{m}}$ b) Equation 17.4 states: $v_{th}=\sqrt{3kt}{m}$ We simplify the above equation to find: $v_{sound} =\sqrt{\frac{1.4 kT}{m}}$ Thus, we find that the percentage is: $\frac{\sqrt{1.4}}{\sqrt3}\times 100 = \fbox{68 percent}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.