The volume V and pressure P of gas in a piston (which vary in time t) satisfy P V 3/2 =

Chapter 3, Problem 84

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The volume V and pressure P of gas in a piston (which vary in time t) satisfy P V 3/2 = C, where C is a constant. Prove that dP /dt dV /dt = 3 2 P V The ratio of the derivatives is negative. Could you have predicted this from the relation P V 3/2 = C?

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