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2 nd Law Cycles Efficiency Heat engines and refrigerators Entropy Kinetic theory of gasses Maxwell’s demon Tiple

# 2 nd Law Cycles Efficiency Heat engines and refrigerators Entropy Kinetic theory of gasses Maxwell’s demon Tiple

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## 2 nd Law Cycles Efficiency Heat engines and refrigerators Entropy Kinetic theory of gasses Maxwell’s demon Tiple

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1. Thermodynamics 2 • 2nd Law • Cycles • Efficiency • Heat engines and refrigerators • Entropy • Kinetic theory of gasses • Maxwell’s demon • Tipler Chapters 18,19,20 Dr Mervyn Roy, S6

2. GAS GAS GAS VACUUM 2nd Law Some processes are allowed by the first law, but never happen… We must be missing something!

3. P V W1 W2 Cyclic process We can extract useful work from a cycle Work out Work in Work extracted W = W1 - |W2 |

4. Efficiency 1st Law Q = ΔU + W P Q2 Q1 W1 In one complete cycle ΔU= 0 Heat in = work extracted + Heat out Q1+ Q2 = (W1–|W2 |) + |Q3+Q4| Qin = W + |Qout| Q3 Q4 W2 V Efficiency = W / Qin

5. Hot reservoir (Th) Qh W |Qc| Cold reservoir (Tc) Heat engine Qh = W + |Qc| Efficiency = W / Qh

6. Hot reservoir (Th) Hot reservoir (Th) Qh |Qh| W W |Qc| Qc Cold reservoir (Tc) Cold reservoir (Tc) Heat engine Refrigerator Qh = W + |Qc| Efficiency = W / Qh W + Qc = Qh COP = Qc / W

7. 2nd Law Perfect refrigerator Hot reservoir (Th) |Qh| W=0 Qc=|Qh| Qc Cold reservoir (Tc) Not allowed! It is impossible for a refrigerator working in a cycle to produce no other effect than the transfer of thermal energy from a cold object to a hot object.

8. 2nd Law Perfect refrigerator Perfect heat engine Hot reservoir (Th) Hot reservoir (Th) |Qh| Qh W=0 Qc=|Qh| W Qc=0, Qh=W Qc Cold reservoir (Tc) Cold reservoir (Tc) Not allowed! Not allowed! It is impossible for a refrigerator working in a cycle to produce no other effect than the transfer of thermal energy from a cold object to a hot object. It is impossible for a heat engine working in a cycle to produce no other effect than that of extracting thermal energy from a reservoir and performing an equivalent amount of work.

9. Forbidden by 2nd law. Processes are irreversible GAS GAS GAS VAC Entropy In any irreversible process the system plus its surroundings move to a less ordered state. ‘Less ordered’ means the ability to do work has been lost. Entropy, S, measures disorder. S is a state variable like U, P, V, T etc. For any process the entropy of the universe never decreases

10. Highest efficiency possible? P Carnot engine: Most efficient engine that can operate between two thermal reservoirs. Qin adiabatic isothermal Efficiency = 1 - |Qout|/ Qin Highest efficiency possible = 1 – TC / Th e.g. Steam Engine. Efficiency = 1 – 273/373 adiabatic Qout isothermal V SeaGen: 1.2 MW from tides in and out of Strangford Lough (N.I.) through the Narrows. The turbine rotor blades can be pitched through 180 degrees allowing them to operate in both flow directions – on ebb and flood tides.

11. Feel the Entropy! 1st Law: W = dU + Q Ideal gas Ideal gas Area A F piston Elastic band

12. From each collision, Force, Pressure, Considering the no. of particles which hit wall in Kinetic Theory Have related microscopic motion to macroscopic variables! Relates temperature to average molecular speed Equipartition of Energy: energy shared equally (kT/2) between all DOF (explains value of cv in an ideal gas)

13. Maxwell-Boltzman distribution • not all molecules in a gas have the same speed • distribution of speeds, , from statistical mechanics dv

14. Maxwell-Boltzman distribution • Hydrogen, m=mp

15. Maxwell-Boltzman distribution • Hydrogen, m=mp

16. Maxwell-Boltzman distribution • Hydrogen, m=mp

17. GAS GAS GAS VACUUM 2nd Law 2nd law is valid statistically High order = low probability Low order = high probability is possible, it is just highly improbable the larger (more macroscopic) the system, the more improbable. 10 molecules, P=1/1024. 20 molecules, P=1/1048576.

18. Maxwell’s Demon

19. Maxwell’s Demon

20. PA2001: Time and Energy Maxwell’s Demon ? Thermodynamics

21. PA2001: Time and Energy Maxwell’s Demon Thermodynamics