Stuf for skool

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.
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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