Chemistry 391
Fall 2007
Problem Set 2
(Due, Monday September 10)
1. Starting with the van der Waals equation of state, find an expression for the total
differential
dP
in terms of
dV
and
dT
.
Calculate the appropriate mixed partial derivatives
and decide if
dP
is an exact differential.
2.
A
differential
( ) ( )
,,
dz
f x y dx
g x y dy
=+
is
exact
if
the
integral
()
f
x y dx
g x y dy
+
∫∫
is independent of the path.
Demonstrate that the differential
2
2
dz
xydx
x dy
is exact by integrating
dz
along the paths:
a) (1,1)
→
(5,1)
→
(5,5), and
b) (1,1)
→
(3,1)
→
(3,3)
→
(5,3)
→
(5,5).
(The first/second number in each set of parentheses is the
x
/
y
coordinate.)
3. Derive the following expression for calculating the isothermal change in the constant
volume heat capacity:
2
2
.
V
T
V
CP
T
VT
⎛⎞
∂∂
=
⎜⎟
⎝⎠
You will need the thermodynamic identity
(we will derive it later)
TV
UP
TP
=−
. Hint: consider the definition of
V
C
.
4. A bottle at 21.0ºC contains an ideal gas at a pressure of 126.4 x 10
3
Pa.
The rubber
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 Fall '08
 Cuckier
 Thermodynamics, 106 Pa, 103 Pa, total differential dP

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