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Chem 6B Equation Sheet (Exam 2)
1
Prof. Crowell
Chem 6B Exam 2 Equation Sheet
1st Law
:
the total amount of energy in the universe is constant (energy is conserved).
Uqw
∆=+
2nd Law
:
in any spontaneous change the entropy of the universe increases.
0
universe
S
∆
>
3rd Law
: the entropy of any pure, perfect crystalline solid at absolute zero is zero.
system
S0
0
at
K
=
D
Ideal gas law:
; First law of thermodynamics:
;
ext
P
Vn
R
T
Uqww PV
=∆
=
+
=
−
∆
Isothermal
⇒
Constant
Temperature
with corresponding changes in Pressure
, Volume
, and with Heat
added
or removed.
;l
n
(
/
)
;
0
0
final
init
P
Vc
o
n
s
tw n
R
T V V
T
U
q w
==
−
∆
=
⇒
∆
=
⇒
=
−
Isobaric
⇒
Constant
Pressure
with corresponding changes in Volume
, Temperature
, and with Heat
added or
removed.
,,
;;
Pm
w
P V
q nC
T
U q w
P V nC
T
=− ∆
=
∆
∆ = +
=− ∆ +
∆
Isosteric
(or Isochoric
)
⇒
Constant
Volume
with corresponding changes in Pressure
, Temperature
, & with
Heat
added or removed.
0s
in
c
e
0
;
;
Vm
pm
wV
q
n
C
T
U
q
w
n
C
T
=
=
∆
∆
=
+
=
∆
Adiabatic
⇒
Constant
Heat
(No Heat Flow)
with corresponding changes in Pressure
, Volume
, and
Temperature
.
P
V
C
1
constant;
=
;
0
C
P
Vq
U
w
U
w
n
R
T
γ
α
γα
+
=
=
=⇒∆= ∆= =
∆
Heat is the transfer of energy as a result of a temperature difference.
Exothermic processes release heat &
Endothermic processes absorb heat.
Calorimetry is the measurement of heats of rxn using heat capacity:
mS
Heat Capacity: C =
; Molar Heat Capacity: C =
; Specific Heat Capacity: C =
(constant volume)
;
(constant pressure)
V
P
VP
qq
q
Tn
T
m
T
q
q
UH
CC
C
C
TT
∆∆
∆
=
=
∆
∆
Enthalpy:  A state function that is a measure of the energy (heat) associated with a constant pressure
process.
Enthalpy
=
,
(
)
H
UP
V H U
P
V
=+
∆=
∆+
∆
For an Ideal Gas:
∆
H =
∆
U +
∆
(PV) =
∆
U +
∆
(nRT) =
∆
U + nR
∆
T
(at const # moles)
⇒
C
P
= C
V
+ nR
∆
U (atom) =
∆
U
translation
∆
U (molecule) =
∆
U
translation
+
∆
U
rotation
+ …
∆
U
vibration
35
Atoms (translational motion only):
;
22
57
Diatomic Molecules (trans., rot., & at high T, vib. contributions):
... ;
...
Linear Polyatomic Molecules (trans., rot., & vib. cont
V
CR
C
C
R
R
R
R
+
=
rib.):
...(3
5) ;
...(3
5)
Nonlinear Polyatomic Molecules (trans., rot., and vib. contrib.):
3
...(3
6) ;
4
...(3
6)
C
R
NR
C
R
C
R
C
R
−
−
−
−
Chapter 7:
Boltzmann's formula for statistical entropy:
ln
S
kW
=
;
W
=
# of microstates
Definition of entropy:
rev
q
S
T
;
fus
vap
fus
vap
mb
HH
SS
∆
∆
⇒∆
=
∆
=
Trouton's Rule
: ∆
S
vap
°
≈
85 J/Kmol
Change in entropy when a substance of constant heat capacity C is heated from
to
:
ln
final
init
final
m
init
T
S
n
C
T
0
()
( )
(
0
)
T
fus
vap
PP
P
C
s dT
C liq dT
C
g dT
ST S
T
T
T
+
+
+
+
∫∫
∫
Change in entropy when an ideal gas expands isothermally from V to V :
ln
ln
final
init
if
init
final
V
P
Sn
R
n
R
=
Change in the surroundings' entropy for a process involving a system enthalpy change
H:
sys
surr
H
S
T
−∆
=
1
(
)
;
Spontaneous if
0
or
0
sys
sys
univ
sys
surr
sys
sys
sys
univ
sys
HG
H
T
S
S
G
T
∆−
∆
−
∆
=
∆
=
=
∆
−
∆
=
⇒
∆
>
∆
<
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View Full DocumentChem 6B Equation Sheet (Exam 2)
2
Prof. Crowell
∆
S
total
=
∆
S
system
+
∆
S
surr
=
∆
S
sys
−
∆
H
sys
/ T;
Reversible Processes:
∆
S
total
= 0;
Irreversible
Processes:
∆
S
total
>
0;
∆
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This note was uploaded on 04/07/2008 for the course CHEM 6B taught by Professor Crowell during the Winter '08 term at UCSD.
 Winter '08
 Crowell

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