Winter 2010
Chemistry 456
First Examination
January 29, 2010
Useful information and equations:
Law IA:
U
q
w
Δ
=
+
Law IB:
( ,
)
V
T
U
U T V
U
U
dU
dT
dV
T
V
=
∂
∂
⎛
⎞
⎛
⎞
=
+
⎜
⎟
⎜
⎟
∂
∂
⎝
⎠
⎝
⎠
H
U
PV
=
+
Heat Capacity
V
V
U
C
T
∂
⎛
⎞
=
⎜
⎟
∂
⎝
⎠
P
P
H
C
T
∂
⎛
⎞
=
⎜
⎟
∂
⎝
⎠
Work:
ext
w
P dV
= −
2
10 m/sec
w
mgh
g
w
VIdt
=
=
=
Kinetic Energy:
2
2
mv
ε
=
Isothermal Reversible work:
ln
f
i
V
w
nRT
V
⎛
⎞
= −
⎜
⎟
⎝
⎠
PV
Const
=
Adiabatic Reversible work:
w
PdV
= −
(
)
,
,
;
where
P m
V m
C
P V
Const
C
γ
γ
=
=
Thermodynamic Equations of State
T
V
T
P
U
P
T
P
V
T
H
V
V
T
P
T
∂
∂
⎛
⎞
⎛
⎞
=
−
⎜
⎟
⎜
⎟
∂
∂
⎝
⎠
⎝
⎠
∂
∂
⎛
⎞
⎛
⎞
=
−
⎜
⎟
⎜
⎟
∂
∂
⎝
⎠
⎝
⎠
Thermal expansion and compression
coefficient
1
1
P
T
V
V
V
T
V
P
β
κ
∂
−
⎛
⎞
⎛
⎞
=
=
⎜
⎟
⎜
⎟
∂
∂
⎝
⎠
⎝
⎠
∂
IG EoS (and other IG relations)
m
PV
RT
=
,
,
P m
V m
C
C
R
=
+
V
P
U
C
T
H
C
T
Δ
=
Δ
Δ
=
Δ
vdW EoS
2
m
m
RT
a
P
V
b
V
=
−
−
Cyclic rule:
1
y
x
z
dx
dz
dy
dy
dx
dz
⎛
⎞
⎛
⎞ ⎛
⎞
= −
⎜
⎟ ⎜
⎟ ⎜
⎟
⎝
⎠ ⎝
⎠
⎝
⎠
Calculus Rules:
(
)
( )
( )
d yz
d y
d z
z
y
dx
dx
dx
dx
dy dx
dz
dz dy
=
+
=
f
i
x
y
x
Z
Z
dx
x
∂
⎛
⎞
Δ
=
⎜
⎟
∂
⎝
⎠
∫
Gas Constant:
8.3
/
0.082
/
300
2.5
/
100
1
R
J
mol
K
R
L
Atm
mol
K
R
K
kJ
mol
J
L
Atm
=
−
=
−
−
⋅
=
≈
−
5
1
1
10
Atm
bar
Pa
≈
=
(
)
(
)
273.15
T K
T C
=
+
The mean is often quite low on my exams.
If you are having difficulty, don’t freak out.
Many parts of problems can be done independently, so if you get stuck, see if you can do another
section.
The questions are not arranged in order of difficulty.
Show your work throughout, always
write down the equations you are using before substituting
in numerical values and always
show units for computed quantities. Show the analytical results
of derivatives and integrals before substituting numbers. You do not need to compute the final
number if you do not want to but show where the numbers you are given can be used.
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 Spring '08
 Staff
 Chemistry, Physical chemistry, Thermodynamics, pH, dy dx Isothermal, Adiabatic Reversible work

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