Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Lecture 5 – The Second Law (Ch. 2)Lecture 5 – The Second Law (Ch. 2)Wednesday January 16Wednesday January 16thth•Brief review of last class (adiabatic processes)•The ideal gas and entropy•The second law•The Carnot cycle•A new function of state - entropyReading: Reading: All of chapter 2 (pages 25 - 48)All of chapter 2 (pages 25 - 48)Homework 1 due this Friday (18th)Homework 1 due this Friday (18th)Homework 2 due next Friday (25th)Homework 2 due next Friday (25th)Homework assignments available on Homework assignments available on web pageweb pageAssigned problems, Assigned problems, Ch. 1Ch. 1: 2, 6, 8, 10, : 2, 6, 8, 10, 1212Assigned problems, Assigned problems, Ch. 2Ch. 2: 6, 8, 16, 18, : 6, 8, 16, 18, 2020Heat capacityHeat capacityUsing the first law, it is easily shown that:VV VđQ UCdq q�� � � �� =� � � ��� � � �( )00 0 andV V VdUC U U U C d Cdqqq q qq� D = - = = -�•For an ideal gas, U = f n() only. Therefore,Always trueAlways true•Enthalpy, H = U + PV, therefore:PP PđQ HCdq q�� � � �� =� � � ��� � � �Always trueAlways truedH = dU + PdV + VdP = đQ + VdP( )00 0 and P P PdHC H H H C d CdTqqq q q� D = - = = -�Ideal gas:Calculation of work for a reversible Calculation of work for a reversible processprocessarea under curve;W PdV=- =�( )UD =�đQ + đWPV(1)(2)(3)(4)1. Isobaric (P = const)2. Isothermal (PV = const)3. Adiabatic (PV = const)4. Isochoric (V = const)•For a given reversible path, there is some associated For a given reversible path, there is some associated physics.physics.Configuration Work Configuration Work onon an ideal gas an ideal gas( )0 IsochoricIsobaricln Isothermalfif iVfViW PdVW P dV P V VVdVW PdV nR nRV Vq q=- ==- =- -� �=- =- =-� �� ���� �Note: for an ideal gas, U = U(), so W = Q for isothermal processes.It is also always true that, for an ideal gas, ( ) ( )andV f i P f iU C H Cq q q qD = - D = -Adiabatic processes: đQ = 0, so W = U, also PV = constant.( ) ( )11V f i f f i iW C P V PVq qg� = - = --3 5 5 5 7 7Monatomic: ; ; Diatomic: ; ;2 2 3 2 2 5P PV P V PV VR R c R R cc c c cc cg g� �= = = = = = = =� �� �Chapter 2Chapter 2100% Conversion of Heat to Work100% Conversion of Heat to WorkMMQQ22W = QW = Q•Heat in equals heat out; energy is conserved! However, common sense tells us this will not work (or it will in a while).100%100% transfer of heat to from cold to hot transfer of heat to from cold to hot bodybodyMMQQ11QQ1122 > > 1111 < < 22•Heat in equals heat out; energy is conserved! But we know this never happens in the real world.Something is Something is clearly missing clearly missing from the first law!from the first law!The Second Law of ThermodynamicsThe Second Law of Thermodynamics•Clausius’ statement: Clausius’ statement: It is impossible to construct a device It is impossible to construct a device that operates in a cycle and whose sole effect is to transfer that operates in a cycle and whose sole effect is to transfer heat from a cooler body to a hotter body.heat from a cooler body to a hotter body.•Kelvin-Planck statement: Kelvin-Planck statement: It is impossible to construct a It is impossible to construct a device that operates in a cycle and produces no other effect device that operates in a cycle and produces no other effect than the performance of work and the exchange of heat than the performance of work and the exchange of heat from a single reservoir.from a single reservoir.•Carnot’s theorem: Carnot’s theorem: No engine operating between two No engine operating between two reservoirs can be more efficient than a Carnot engine reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs.operating between the same two reservoirs.Heat reservoir at Heat reservoir at temperature temperature 22 > > 11Cold reservoir at Cold reservoir at temperature temperature 11 < < 22HeatHeatEngineEngineQQ22QQ112 12 1W Q QQ Q= +-Q  heatW  workboth in JoulesConversion of Heat to Work (a heat Conversion of Heat to Work (a heat engine)engine)*Be careful with the signs for heat!Efficiency (*):2 2outputinputWWQ Qh = = =2 1 12 21Q Q QQ Qh+= = +121QQh = -**The Carnot CycleThe Carnot Cycle1.1. aabb isothermal expansion isothermal expansion2.2. bbcc adiabatic expansion adiabatic expansion3.3. ccdd isothermal compression isothermal compression4.4. ddaa adiabatic compression adiabatic compression1.1. WW22 > 0, > 0, QQ22 > 0 (in) > 0 (in)2.2. WW'' > 0, > 0, QQ = 0 = 03.3. WW11 < 0, < 0, QQ11 < 0 (out) < 0 (out)4.4. WW'''' < 0, < 0, QQ = 0 = 0121qhq= -•Stirling’s engine is a good approximation to Carnot’s cycle.2q1qVThe Carnot CycleThe Carnot Cycle1.1. aabb isothermal expansion isothermal expansion2.2. bbcc adiabatic expansion adiabatic expansion3.3. ccdd isothermal compression isothermal compression4.4. ddaa adiabatic compression adiabatic compression1.1. WW22 > 0, > 0, QQ22 > 0 (in) > 0 (in)2.2. WW'' > 0, > 0, QQ = 0 = 03.3. WW11 < 0, < 0, QQ11 < 0 (out) < 0 (out)4.4. WW'''' < 0, < 0, QQ = 0 = 0121TTh = -•Stirling’s engine is a good approximation to Carnot’s cycle.V0 100 200 300 400PressureTemperature (K)TT(K)(K) = T = T((ooC) + 273.15C) + 273.15The ‘absolute’ temperature (Kelvin) The ‘absolute’ temperature (Kelvin) scalescaleTriple pointof water:273.16 KBased on the Based on the ideal gas lawideal gas law01020-300 -250 -200 -150 -100 -50 0 50 100T = aP + bValue Errorb -267.2 2.8a 19.5 0.2 = 2.2 Data Linear fit Temperature (oC)Pressure (arb. units) P T17.7 7913.8 03.63 -195.97An experiment that I did in PHY3513An experiment that I did in PHY3513The Second Law of ThermodynamicsThe Second Law of Thermodynamics•Clausius’ statement: Clausius’ statement: It is impossible to construct a device It is impossible to construct a device that operates in a cycle and whose sole effect is to transfer that operates in a cycle and whose sole effect is to transfer heat from a cooler body to a hotter body.heat from a cooler body to a hotter body.•Kelvin-Planck statement: Kelvin-Planck statement: It is impossible to construct a It is impossible to construct a