1. Chapter 18 Second Law of Thermodynamics

2. Introduction 2 First law → conservation of energy Processes that conserve energy may not occur 400K300K heat Some process occurs spontaneously, but its inverse process can not. It is about the second law of thermodynamics

3. working substance Heat engines 3 (1) High T H & Low T L (2) Run in a repeating cycle P V QHQH QLQL W

4. Engine efficiency 4 Efficiency of heat engine: P V QHQH QLQL W Counterclockwise cycle: Coefficient of performance Refrigerator

5. Reversible & irreversible processes 5 Reversible process: can be done in reverse with no change in magnitude of W and Q 2 1 P V 2 1 No friction, quasi-static reverse in the same path Ideal model as well Real processes are irreversible Friction, turbulence, … no PV diagram!

6. Efficiency of engine 6 Example1: The PV diagram shows a reversible heat engine. Calculate the efficiency. Solution: V V2V P A C B isothermal isobaric isochoric working substance: Argon (Ar)

7. Efficiency of another engine 7 Homework: The PV diagram shows a reversible heat engine. Calculate the efficiency. V V2V P A C B adiabatic isobaric isochoric working substance: Argon (Ar)

8. Carnot engine 8 N. L. Carnot: make use of Carnot cycle: a b c d

9. Carnot’s theorem 9 The efficiency of a Carnot engine depends only on the temperature T L and T H. All reversible engines operating between the same two constant temperature T H and T L have the same efficiency. Any irreversible engine will have an efficiency less than this. —— Carnot’s theorem

10. 2 nd law of thermodynamics (1) 10 No device is possible that the only effect is to transform heat completely into work. Kelvin-Planck statement of the second law: Or: There is no perfect (e=100%) heat engine. Carnot’s theorem: → 3 rd law of thermodynamics Energy sources & thermal pollution

11. False advertising 11 Example2: An engine manufacturer claims that: The heat input the engine is 9kJ/s at 200 ℃, the heat output is 4kJ/s at 30 ℃. Do you believe it? Solution: The efficiency of the engine is The maximum possible efficiency: can’t be believed

12. 2 nd law of thermodynamics (2) 12 P V QHQH QLQL W Coefficient of performance For an ideal refrigerator: No device is possible whose only effect is to transfer heat from a low T system into a high T system. Clausius statement of the 2 nd law:

13. Equivalence of two statements 13 If the Kelvin statement is violated W=QH W=QH THTH QH QH QH+QL QH+QL TLTL QLQL THTH TLTL QLQL The Clausius statement is also violated So Clausius → Kelvin, and vice-versa

14. Refrigerator & Heat pump 14 Example3: It is -7 ℃ inside an ideal refrigerator working in a 27 ℃ room. (a) How much work is done to take 1000J from food inside it? (b) How much heat flows to the room? Solution: (a) Coefficient of performance Work done: (b) Heat pumped:

15. Entropy (1) 15 General statement of 2 nd law by using a quantity Heats flow into system: Carnot’s cycle: p V For any reversible cycle:

16. Entropy (2) 16 p V a. b. c d Integral between a and b not depend on path! Define a new quantity “entropy”:

17. Entropy (3) 17 1) Entropy is a state variable. 2) Need not to know the absolute value of S Key point is ΔS, like the potential energy 3) For irreversible process: Still have:

18. Mixing water 18 Example4: 1kg water at 20 ℃ is mixed with 1kg water at 80 ℃. Calculate the change in entropy. Solution: 20 ℃ → 50 ℃ : 80 ℃ → 50 ℃ : Net change in entropy:

19. Free expansion 19 Example5: Adiabatic free expansion from V to 2V. Calculate the change in entropy. Solution: Reversible process: same T, V → 2V V i.. f P isothermal ΔS for the environment?

20. Entropy Increase Principle 20 Reversible process: Irreversible process: The entropy of an isolated system never decreases. Or: The total entropy of any system plus that of its environment increases in any natural process. Quantitative general statement of the 2 nd law: Also noted as the principle of entropy increase

21. Order to disorder (1) 21 Entropy: a measure of the disorder of system Natural processes tend to move toward a state of greater disorder.

22. Order to disorder (2) 22 ordered energy → disordered energy 400K300K heat different average energy → same average energy.......................... ordered position → disordered position

23. Living beings & entropy 23 A living being is an ordered system It needs negative entropy (by E. Schrödinger) Food & excretion → metabolism solar energy light H 2 O, CO 2, … waste heat sugar fat, … waste heat human body, civilizations O2O2 Circle of life