Thermodynamics, Statistical Thermodynamics, & Kinetics
Thermodynamics, Statistical Thermodynamics, & Kinetics
3rd Edition
ISBN: 9780321766182
Author: Thomas Engel, Philip Reid
Publisher: Prentice Hall
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Chapter 3, Problem 3.38NP

Show that C V V T = T 2 P T 2 V

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Since we will be dealing with partial derivatives later in the semester, this is a good opportunity to review this topic (see appendix C). Then evaluate the following partial derivatives (a) PV = nRT;        (∂ P/∂V)T (b) r = (x2 + y2 + z 2 )1/2;   (∂ r/∂y)x,z
Show that CP = VT α (∂P/∂T) S
Rearrange the van der Waals equation of state, p = nRT/(V − nb) − n2a/V2(Topic 1C) to give an expression for T as a function of p and V (with n constant). Calculate (∂T/∂p)V and confirm that (∂T/∂p)V = 1/(∂p/∂T)V.

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Thermodynamics, Statistical Thermodynamics, & Kinetics

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