Unformatted text preview: ) ) , ( ∂ ( ∂f ) ) .
∂x y ∂y x ∂x 2
∂y 2
∂y ∂x y
∂x ∂y x
y
x
x
y
∂ ∂f
∂ ∂f
Is ( ( ) ) = ( ( ) ) ?
∂y ∂x y
∂x ∂y x
x
y
7.
Equation 3.38, C P = C V + TV(β 2 /κ)
links CP and CV with β and κ. Use this equation to evaluate CP
CV for an ideal gas. 8.
Starting with the van der Waals equation of state, find an expression for the total differential dP in terms of dV and dT. By calculating the mixed partial derivatives of P with respect to V and T, determine in dP is an exact differential. 9.
Because V is a state function, (∂(∂V/∂P) T /∂T) P = (∂(∂V/∂T) P /∂P) T
Using this relationship, show that the isothermal compressibility and isobaric expansion coefficient are related by: (∂β/∂P) T = −(∂κ/∂T) P
10.
For an ideal gas, ∂U
∂H
(
) and (
) =0
∂V T
∂P T
Prove that CV is independent of volume and that CP is independent of pressure. Extra Problems for your own study – NOT TO BE HANDED IN! These are not part of the assignment, but I will post their solutions with the assignment solutions after the due date. Of course, you can also do any of the questions in red at the end of the chapters if you also have access to the Student Solutions Manual. st edition: Engel and Reid, 1
Q1.1, P1.17 Q2.5, Q2.8, P2.2, P2.5, P2.10, P2.22, P2.24, P2.25, P2.26, P2.28 Q3.7, P3.1, P3.3, P3.9, P3.16, P3.18, P3.21, P3.30 Engel and Reid, 2nd edition: Q1.3, Q1.6, P1.35 Q2.2, Q2.8, P2.11, P2.21, P2.29, P2.32, P2.33, P2.35, P2.39, P2.43 Q3.1, P3.3, P3.8, P3.12, P3.16, P3.24, P3.28, P3.31...
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