Page 89 - Physical chemistry eng

66 CHAPTER 3 The Importance of State Functions: Internal Energy and Enthalpy

P3.28 Use the relation P3.32 Regard the enthalpy as a function of T and P. Use the
cyclic rule to obtain the expression
0V m 0P
C P,m - C V,m = Ta b a b
0T P 0T V C =- a 0H b n a 0T b
P
the cyclic rule, and the van der Waals equation of state to 0P T 0P H
derive an equation for C P, m – C V, m in terms of V , T, and the P3.33 Using the chain rule for differentiation, show that the
m
gas constants R, a, and b. isobaric expansion coefficient expressed in terms of density is
P3.29 For the equation of state V m = RT>P + B(T) , given by b =-1>r(0r>0T) P .
show that P3.34 Derive the equation (0P>0V) =-1>(kV) from
T
2
0C P,m d B(T) basic equations and definitions.
a b =-T
0P T dT 2 P3.35 Derive the equation (0H>0T) = C + Vb>k from
V
V
basic equations and definitions.
[Hint: Use Equation (3.44) and the property of state functions 0U 0H
with respect to the order of differentiation in mixed second P3.36 For an ideal gas, a b and a b = 0 . Prove
0V T 0P T
derivatives.]
that C and C are independent of volume and pressure.
V
P
P3.30 Starting with b = (1>V)(0V>0T) P , show that P3.37 Prove that C =- a 0U b a 0V b
r =-(1>r)(0r>0T) P , where is the density. V 0V T 0T U
r
P3.31 This problem will give you practice in using the 0C V 0 P
2
cyclic rule. Use the ideal gas law to obtain the three func- P3.38 Show that a b = Ta 2 b
0V T 0T V
tions P = f(V, T) , V = g(P, T) , and T = h(P, V) . Show
that the cyclic rule (0P>0V) (0V>0T) (0T>0P) =-1 P3.39 Show that a 0C V b = 0 for an ideal and for a van der
P
V
T
is obeyed. Waals gas. 0V T