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

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**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**GAS**GAS GAS VACUUM 2nd Law Some processes are allowed by the first law, but never happen… We must be missing something!**P**V W1 W2 Cyclic process We can extract useful work from a cycle Work out Work in Work extracted W = W1 - |W2 |**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**Hot reservoir (Th)**Qh W |Qc| Cold reservoir (Tc) Heat engine Qh = W + |Qc| Efficiency = W / Qh**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**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.**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.**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**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.**Feel the Entropy!**1st Law: W = dU + Q Ideal gas Ideal gas Area A F piston Elastic band**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)**Maxwell-Boltzman distribution**• not all molecules in a gas have the same speed • distribution of speeds, , from statistical mechanics dv**Maxwell-Boltzman distribution**• Hydrogen, m=mp**Maxwell-Boltzman distribution**• Hydrogen, m=mp**Maxwell-Boltzman distribution**• Hydrogen, m=mp**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.**PA2001: Time and Energy**Maxwell’s Demon ? Thermodynamics**PA2001: Time and Energy**Maxwell’s Demon Thermodynamics