The volume V and pressure P of gas in a piston (which vary in time t) satisfy

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The volume V and pressure P of gas in a piston (which vary in time t) satisfy PV3/2 = C, where C is a constant. Prove that

dp/dt dv/dt ||  3 P 2 V

The ratio of the derivatives is negative. Could you have predicted this from the relation PV3/2 = C?

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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