In physical chemistry, it is shown that the pressure P of a gas is related to the

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In physical chemistry, it is shown that the pressure P of a gas is related to the volume V and temperature T by van der Waals’ equation:


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where a, b, n, and R are constants. The critical temperature Tc of the gas is the highest temperature at which the gaseous and liquid phases can exist as separate phases.


a. When T = Tc, the pressure P is given as a function P(V) of volume alone. Sketch the graph of P(V).


b. The critical volume Vc is the volume for which P'(Vc) = 0 and P"(Vc) = 0. Show that Vc = 3b.


c. Find the critical pressure Pc = P(Vc) and then express Tc in terms of a, b, n, and R.

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Calculus For Business, Economics And The Social And Life Sciences

ISBN: 9780073532387

11th Brief Edition

Authors: Laurence Hoffmann, Gerald Bradley, David Sobecki, Michael Price

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