1. PA2001: Time and Energy Thermodynamics 2 nd Law Cycles Efficiency Heat engines and refrigerators Entropy Kinetic theory of gasses Maxwell’s demon Tipler Chapters 18,19,20 Thermodynamics 2 Dr Mervyn Roy, S6

2. PA2001: Time and Energy Thermodynamics 2 nd Law Some processes are allowed by the first law, but never happen… GASVACUUM GAS We must be missing something!

3. PA2001: Time and Energy Thermodynamics Cyclic process P V W1W1 W = W 1 - |W 2 | W2W2 We can extract useful work from a cycle Work outWork inWork extracted

4. PA2001: Time and Energy Thermodynamics Efficiency P V Q1Q1 Q2Q2 Q4Q4 Q3Q3 W1W1 W2W2 In one complete cycle ΔU = 0 Heat in = work extracted + Heat out Q 1 + Q 2 = (W 1 –|W 2 |) + |Q 3 +Q 4 | Q in = W + |Q out | Efficiency = W / Q in 1 st Law Q = ΔU + W

5. PA2001: Time and Energy Thermodynamics Heat engine QhQh |Q c | W Cold reservoir (T c ) Hot reservoir (T h ) Q h = W + |Q c | Efficiency = W / Q h

6. PA2001: Time and Energy Thermodynamics QhQh |Q c | W Cold reservoir (T c ) Hot reservoir (T h ) |Q h | QcQc W Cold reservoir (T c ) Hot reservoir (T h ) Refrigerator W + Q c = Q h COP = Q c / W Q h = W + |Q c | Efficiency = W / Q h Heat engine

7. PA2001: Time and Energy Thermodynamics |Q h | QcQc W=0 Q c =|Q h | Cold reservoir (T c ) Hot reservoir (T h ) Not allowed! Perfect refrigerator 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. 2 nd Law

8. PA2001: Time and Energy Thermodynamics |Q h | QcQc Cold reservoir (T c ) Hot reservoir (T h ) Not allowed! QhQh W Cold reservoir (T c ) Hot reservoir (T h ) Perfect refrigerator 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. Perfect heat engine Q c =0, Q h =W Not allowed! 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. W=0 Q c =|Q h | 2 nd Law

9. PA2001: Time and Energy Thermodynamics Entropy Forbidden by 2 nd law. Processes are irreversible 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. GASVACGAS 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. PA2001: Time and Energy Thermodynamics Highest efficiency possible? Carnot engine: Most efficient engine that can operate between two thermal reservoirs. P V Q in Q out adiabatic isothermal 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. Efficiency = 1 - |Q out |/ Q in Highest efficiency possible = 1 – T C / T h e.g. Steam Engine. Efficiency = 1 – 273/373

11. PA2001: Time and Energy Thermodynamics Feel the Entropy! Area A Ideal gas F piston 1 st Law: W = dU + Q Ideal gas Elastic band

12. PA2001: Time and Energy Thermodynamics 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 c v in an ideal gas) From each collision, Force, Pressure, Considering the no. of particles which hit wall in

13. PA2001: Time and Energy Thermodynamics Maxwell-Boltzman distribution not all molecules in a gas have the same speed distribution of speeds,, from statistical mechanics dv

14. PA2001: Time and Energy Thermodynamics Hydrogen, m=m p Maxwell-Boltzman distribution

15. PA2001: Time and Energy Thermodynamics Hydrogen, m=m p Maxwell-Boltzman distribution

16. PA2001: Time and Energy Thermodynamics Hydrogen, m=m p Maxwell-Boltzman distribution

17. PA2001: Time and Energy Thermodynamics 2 nd Law GASVACUUMGAS 2 nd 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. PA2001: Time and Energy Thermodynamics Maxwell’s Demon

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

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

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