Stuf for skool

Topics: Entropy, Thermodynamics, Adiabatic process Pages: 6 (1014 words) Published: October 17, 2014
Chapter 3
The second law
Physical Chemistry. Atkins 9th ed.

1

Outcomes
• Concepts
1. The second law of thermodynamics: Spontaneous changes, Entropy (ΔS), Heat engine (Carnot cycle), Clausius inequality.
2. Entropy changes: ΔS of expansion, ΔS of phase transitions, ΔS during heating, measuring entropy, the 3rd law of thermodynamics, 3rd law entropies.
3. Criteria for spontaneity: Helmholtz energy (A), Gibbs energy (G), Maximum work (ΔA), maximum non-expansion work (ΔG).

4. Combining the 1st and 2nd laws: The fundamental equations, U as a function of S and V, H as a function of S and p, G as a function of p and T, A as a function of V and T, definitions of T, p, V and S, Maxwell relations 5. Focus on Gibbs energy: ΔrxnGo, ΔG during heating (Gibbs-Helmholtz equation), ΔG with pressure changes, Fugacity and the standard state. 2

Equations and Flow Chart
rev, isotherm, expansion, ideal
gas
dV
dU  0 so q  w  nRT
V

Entropy (definition):
As shown in
Carnot cycle

dS 

qrev
T

Rearranged for
integration.
S2

 dS  

S1

qrev

rev, isobaric,
heating, ideal gas

T

How to integrate?

S2

T2

S1

V2

S1

V1

dV

 dS  nR  V

T1

 dS  

q p  dH  C p dT

S2

C p dT

S  nR ln

T2

Cp indepenent of T

dT
T
 a ln 2
T
T1
T1

S  a 

Cp  a

T

V2
V1

Carnot Cycle:
1st law for perfect gas with only pdV work
nRT
CV dT  q 
dV
V
Rearrange for cyclic integration
dT
q
dV
CV 
   nR 
T
T
V
Integrate each over 4 stage Carnot cycle
1. Reversible isothermal expansion, A to B
2. Reversible adiabatic expansion, B to C
3. Reversible isothermal compression, C to D
4. Reversible adiabatic compression, D to E

dT
dV
CV 
 0 and nR 
0
T
V

Cp a function of T
Some examples

T2

2



T

2
dT
T b
S  a 
 b  TdT  a ln 2  T22  T12
T
T1 2
T1
T1



T2

dT
1
 1
  a 2  1 
2
T
T 
T
T1

S  a 

a
C p (T ) 
T
b
C p (T )  a  2
T

Requires a new state function
q
q
 Trev  0 or dS  Trev

S  a  dT  aT
T1

C p (T )  aT
C p (T )  a  bT

T2

2
dT
dT
T b 1
1 
S  a 
 b  3  a ln 2   2  2 
T
T
T
T1 2  2 T1 

T1
T1

T2

T

For non-reversible expansion
use the Clausius inequality

dS 

q
T

3

Equations and Flow Chart
Phase Transition:

Heating with phase changes:

Trouton`s Rule:

 H
 trs S m  trs m
Ttrs

o
 vap S m  85 J K 1 mol 1 

rev, isobaric, heating, ideal gas including phase transitions

o
 vap H m

Sf

 dS 

Tvap

Si

Tf



Ti

C p dT
T

T fus





Ti

C p ( s)dT
T



 fus H
T fus

Tvap





T fus

C p (l )dT
T



 vap H
Tvap

Tf





C p ( g )dT
T

Tvap

3rd law Entropies
Helmholtz energy:

 subS o   vap S o   fus S o

A  U  TS definition

r S o 

 vS

o
m

products



 vS

o
m

 subG o   vapG o   fusG o

dG  dH  TdS  SdT

G o  A  B  G o B  A

dA  dU  TdS

o

G  H  TS definition

dA  dU  TdS  SdT

S  A  B   S B  A
o

Gibbs energy:

dG  dH  TdS

@ fixed T

@ fixed T

reactants

rGo 

 vG
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