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313 Exam 3 Cheat Sheet by

Laws

Zeroth Law: If system x = system y & system y = system z, then system x = system z. (Trans­itive)
First Law: Internal energy(ΔU) of an isolated system is constant. No heat lost, only transf­erred.
Second Law: The entropy of any isolated system always increases.
Third Law: The entropy of a system approaches a constant value as the temper­ature approaches absolute zero.
Cyclic Rule: (dP/dT)
v
(dT/dV)
p
(dV/dP)
T
= -1

Defini­tions

Adiabatic: No transfer of heat or matter
Diathe­rmal: Heat allowed to transfer, no matter transfer. Can transfer energy in the form of work
Enthal­py(ΔH): Amount of heat content used or released in a system at constant pressure
Irreve­rsible: A process that cannot return both the system and the surrou­ndings to their original condit­ions.

Exam 2

ΔU=m
s
/M
s
ΔU
comb
+m
H2O
/M
H2O
C
v,m
(H2O)Δ­T+ΔTC
calori­meter
ΔHo=m
salt
/M
salt
ΔHo
solution
+m
H2O
/M
H2O
C
p,m
(H2O)Δ­T+ΔTC
calori­meter
S=k ln(W) W=#of states
Efficiency = 1-|q
cd
|/|q
ab
| <1
ΔHo
rt
=ΔHo
298
+∫ΔC
p
(T) dT from 298 to T
ΔH
combustion
= ΔU
combustion
+Δ(PV)
For Solids & Liquids: ΔH~= ΔU
Δs=-nRln(P
f
/P
i
)+∫nC
pm
/T dT for P
i
to P
f
Δs=nRln(V
f
/V
i
)+∫nC
vm
/T dT for V
i
to V
f
Isolated System: ΔS=q
p
(1/T
1
- 1/T
2
)
Isothe­rmal, Ideal: ΔS=nRln(V
f
/V
i
)
ΔS
total
=ΔS+ΔS
surrou­ndings
ΔG=nRT Σ x
i
ln(x
i
) x
i
is mole fraction
ΔG = TΔS
total
 

Internal Energy (ΔU)

General
ΔU=q+w
Constant Volume
ΔU=C
v
ΔT = q
v
Adiabatic, Reversible
ΔU= w = n(C
pm
-R)ΔT = nC
vm
ΔT
Ideal
ΔU=nC
vm
ΔT

Enthalpy (ΔH) (State Fxn)

General
ΔH= ΔU+Δ(PV) = ΔU+nRΔT
Constant Pressure
ΔH= C
p
ΔT
Ideal
ΔH = q
p
Constant Volume
ΔH= nC
pm
ΔT + VΔP
Even More General
dH= (dH/dP)
T
dT + (dH/dT)
P
dP
Liquids & Solids
(dH/dP)
T
= V(1-Tβ)
Constant Pressure, closed system
ΔH= (U
f
+P
f
V
f
)-(U
i
+P
i
V
i
)
Isobaric
ΔH= n∫C
pm
(T) dT = nC
pm
ΔT

Exam 2 Material

S
m
(T)=S
m
(0ok) +∫C
pm
/T dT(solid 0-T
f
) +ΔH
fus
/T
f
+ ∫C
pm
/T dT(liquid T
f
-T
b
) +ΔH
vap
/T
b
∫C
pm
/T dT(gas T
b
-T) `
For Ideal Gases: ΔS
m
=Rln(V
f
/V
i
)=-Rln(P
f
/P
i
)
ΔG(T
2
)/T
2
= ΔG(T
1
)/T
1
+ΔH(T
1
)(1/T
2
-1/T
1
)
Max Work: Revers­ible, adiabatic, isothermal
Hess's Law: Total Enthalpy change is indepe­ndent of # of steps(­pat­h-i­nde­pen­dent).
ΔA = ΔU-TΔS = ΔH-nRT (Hemholtz)
for ΔGo
r
only include non-pure substa­nces.

Exam 3

ΔG
R
= ΔG°
R
+RT ln(Q
P
)
ln(K
P
) = -ΔG°
R
/RT
K
x
=K
P
(P/P°)-ΔV
dA = 𝛾 dσ gamma is surface tension
Work = 8pi𝛾r dr
Force = 8pi𝛾r
h(capi­llary rise/d­epr­ession) = 2𝛾/𝞺gr
𝓾
B
=𝓾°
B
+RTln(­𝛾[B]) gamma is activity coeffi­cient
ΔG
R
= ΔG°
R
-2.303­vRT(pH)
q
x
= kA(T
si
-T
so
)/L
q''
x
= -k dT/dx = q
x
/A
Ė
in
+Ė
g
-Ė
out
= Ė
internal
q
12
= εσA(T
1
4-T
2
4) - Heat xchange via radiation b/t 2 surfaces
q''
s
= h(T
s
-T
∞
) - Newton's Law of Cooling
       
 

Metadata

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  • Published: 25th September, 2016
  • Last Updated: 9th December, 2016

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