Chem 6B Equation Sheet (Exam 3)
1
Prof. Crowell
Chem 6B Final Exam Equation Sheet
1st Law
:
the total amount of energy in the universe is constant (energy is conserved).
U
q
w
∆
=
+
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
S
0
0
at
K
=
D
An open system can exchange both matter & energy
with its surroundings. A closed system can exchange
energy
with the surroundings but not matter.
An isolated system cannot exchange energy nor matter.
Diathermic Walls
allow energy to flow as heat if there is a temperature difference between the system &
surroundings, whereas Adiabatic Walls
do not.
Reversible Process
– A process involving a series of
infinitesimal changes
.
At each step in a reversible process, the system is in mechanical equilibrium (e.g. P
or T) with its surroundings.
Irreversible Process
– A process in which change occurs by
finite
amounts.
The work done in the expansion process approaches the reversible process as the number of steps becomes larger.
The maximum work done in an expansion is during a reversible process. Sign convention: heat & work are both
positive when they
enter
the system & negative when they
leave
the system.
Ideal gas law:
;
PV
nRT
=
2
2
3
work = force
distance = Nm = kgm
/s
= Pam
= J;
Expansion work =
ext
w
P
V
×
= −
∆
= −
∆
Isothermal
⇒
Constant
Temperature
with corresponding changes in Pressure
, Volume
, and with Heat
added
or removed.
;
reversible work:
ln
;
0
0
final
init
V
PV
const
w
nRT
T
U
q
w
V
=
= −
∆
=
=
= −
∆
=
=
=
⇒
∆
=
∆
=
∆
∆
⇒
= −
= −
Isobaric
⇒
Constant
Pressure
with corresponding changes in Volume
, Temperature
, and with Heat
added or
removed.
,
,
;
;
P m
P m
w
P
V
q
n C
T
U
q
w
P
V
n C
T
= −
∆
=
∆
∆
=
+
= −
∆
+
∆
= −
∆
+
Isosteric
(or Isochoric
)
⇒
Constant
Volume
with corresponding changes in Pressure
, Temperature
, & with
Heat
added or removed.
,
,
0 since
0;
;
V m
p m
w
V
q
n C
T
U
q
w
n C
T
=
∆
=
=
∆
∆
=
+
=
∆
∆
+
Adiabatic
⇒
Constant
Heat
(No Heat Flow)
with corresponding changes in Pressure
, Volume
, and
Temperature
.
1
P
V
C
1
constant;
also
constant;
V
constant;
with =
;
C
PV
TV
T
γ
γ
α
γ
α
γ
α
+
=
=
=
=
=
Adiabatic:
0
;
using
we find
q
U
w
w
PdV
U
w
n R
T
α
=
⇒
∆
=
= −
∆
=
=
∆
=
∫
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:
m
s
Heat Capacity: C =
;
Molar Heat Capacity: C
=
;
Specific Heat Capacity: C
=
q
q
q
T
n
T
m
T
∆
∆
∆
∆
∆
∆
∆
∆
At Constant Volume
(i.e. using a bomb calorimeter):
∆
U = q + w = q – P
ex
∆
V = q = q
V
At Constant Pressure
(i.e. using a coffeecup calorimeter):
∆
H =
∆
U +
∆
(PV) = q – P
ex
∆
V + P
ex
∆
V = q
P
(constant volume)
;
(constant pressure)
V
P
V
P
q
q
U
H
C
C
C
C
T
T
T
T
∆
∆
∆
∆
=
=
=
=
=
=
=
∆
∆
∆
∆
∆
∆
∆
∆
Enthalpy: A state function that is a measure of the energy (heat) associated with a constant pressure process.
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 Winter '08
 Crowell
 pH, Energy, Entropy, Chem 6B Equation, 6B Equation Sheet

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