1. Entropy & Energy Quality
2nd law:
Energy of higher quality can be converted completely into lower quality form.
But not vice versa.
Energy quality Q measures the versatility of different energy forms.

2. Entropy  Carnot cycle (reversible processes): C = any closed path
Qh = heat absorbed
Qc = heat rejected
lukewarm: can’t do W, Q  
Qh , Qc = heat absorbed
C = any closed path
Irreversible processes can’t be represented by a path.
S = entropy
[ S ] = J / K

3. Entropy  Contour = sum of Carnot cycles.
Carnot cycle (reversible processes):
Qh = heat absorbed
Qc = heat rejected 
Qh , Qc = heat absorbed
lukewarm: can’t do W, Q 
C = Carnot cycle
C = any closed path
Irreversible processes can’t be represented by a path.
S = entropy
[ S ] = J / K
Contour = sum of Carnot cycles.

4. S = 0 over any closed path
 S21 + S12= 0
 S21 = S21
Entropy change is path-independent.
( S is a thermodynamic variable )

5. Entropy in Carnot Cycle
Ideal gas：
Heat absorbed:
Heat rejected:
Adiabatic processes： 

6. Irreversible Heat Transfer
Cold & hot water can be mixed reversibly using extra heat baths.
T1 = some medium T.
reversible processes
T2 = some medium T.
Actual mixing, irreversible processes

7. Adiabatic Free Expansion
Adiabatic  Qad.exp. = 0   
S can be calculated by any reversible process between the same states.
isothermal
p = const.
Can’t do work
Q degraded.

8. Entropy & Availability of Work
Before adiabatic expansion, gas can do work isothermally
After adiabatic expansion, gas cannot do work, while its entropy increases by 
In a general irreversible process
Coolest T in system

9. A Statistical Interpretation of Entropy
Gas of 2 molecules occupying 2 sides of a box
Microstates
Macrostates
probability of macrostate
1/4
2 ¼ = ½
1/4

10. probability of macrostate
Gas of 4 molecules occupying 2 sides of a box
Microstates
Macrostates
probability of macrostate
1/16 = 0.06
4 1/16 = ¼ =0.25
6 1/16 = 3/8 = 0.38
4 1/16 = ¼ =0.25
1/16 = 0.06

11. Gas of 100 molecules
Gas of 1023 molecules
Equal distribution of molecules
Statistical definition of entropy :
 # of micro states

12. Entropy & the 2nd Law of Thermodynamics
in any closed system
S can decrease in an open system by outside work on it.
However, S  0 for combined system.
 S  0 in the universe
Universe tends to disorder
Life ?