1. Chapter 3 The 2nd law of thermodynamics
1st law :
Any thermal process should obey the law of energy conservation！
Is a process possible if it obeys the law of energy conservation?

2. Heat transfer
High
temperature
Low
temperature
Conversion of work into heat
work
heat

3. Gas expansion
uniform
in density
non-uniform
in density
Life process
birth
death
All the real processes in nature related to thermal phenomena should have directions.
2nd law a basic law about the direction of a process

4. §1 The literal statements of the 2nd law
The Kelvin statement
No process is possible whose sole result is the absorption of heat from a single reservoir and the complete conversion of this heat energy into work without producing any other effects in the environment.
perpetual motion machine of type II is impossible
Conversion of work into heat is irreversible

5. The Clausius statement
No process is possible whose sole result is the transfer of heat from a cold to a hot body without producing any other effects in the environment.
A refrigerator is not possible without using work
Heat transfer is irreversible

6. If Kelvin statement fails
Clausius statement fails =

7. If Clausius statement fails
Kelvin statement fails =

8. Equivalence of Clausius and Kelvin statements!
Irreversibility of converting work into heat
Irreversibility of heat transfer
All the irreversibility are consistent!
All the irreversible processes are related and can be derived to each other, which implies that there may be various statements of the 2nd law and all of them are equivalent.
The irreversibility is not determined by the path of a process but by the initial and final states of the system, i.e., it is a function of state (entropy).

9. §2 Carnot theorem and entropy
Carnot’s theorem
The literal statements
The efficiency of an irreversible heat engine operating between two reservoirs (hot and cold) is less than that of any reversible engine operating between the same reservoirs.
The mathematic expressions

10. perpetual motion machine of type II
Prove
perpetual motion machine of type II if = R

11. The Clausius relations
Cyclic process with two reservoirs
If the minus sign is put into Q2, then
By writing so, Q1 and Q2 are the heat “absorbed” from reservoirs with temperature T1 and T2, respectively.
Cyclic process with many reservoirs

12. Prove … … R R R … …
system

13. Cyclic process with many reservoirs
General cyclic process
For reversible cycle A
entropy B
can take any reversible process
extensive state quantity
For irreversible cycle
The principle of increase of entropy

14. §3.3 The principle of increase of entropy
For irreversible cycle A B
mathematic expression of 2nd law
Note：In a reversible process, T can be viewed as the temperature of the system, while it is not in an irreversible process.

15. 1st law ＋ 2nd law
The principle of increase of entropy
For an adiabatic system
It follows that in an adiabatic process the entropy of a system never decreases. It either increases for irreversible process or remains constant for reversible process.
To determine the direction of an irreversible process

16. §4 Calculation of entropy change
Reversible process
adiabatic process
isothermal process
constant-volume process
constant-pressure process
phase transition
Irreversible process
Entropy is a function of state!
Consider a virtual reversible process with the same initial and final states

17. §5 Temperature-entropy plot
Reversible process：
Using T～S plot to calculate heat absorbed:
Using T～S plot to calculate the efficiency of a cyclic process：
ratio of the area!