Page Physics 207 – Lecture 27Physics 207: Lecture 27, Pg 1Lecture 26Goals:Goals:••Chapters 18, entropy and second law of thermodynamicsChapters 18, entropy and second law of thermodynamics••Chapter 19, heat engines and refrigeratorsChapter 19, heat engines and refrigerators•No lab this week. Physics 207: Lecture 27, Pg 2Equipartition theoremlThings are more complicated when energy can be stored in other degrees of freedom of the system. monatomic gas: translationsolids: translation+potential energydiatomic molecules: translation+vibrations+rotationsPage Physics 207 – Lecture 27Physics 207: Lecture 27, Pg 3Equipartition theoremlThe thermal energy is equally divided among all possible energy modes (degrees of freedom). The average thermal energy is (1/2)kBT for each degree of freedom. εavg=(3/2) kBT (monatomic gas)εavg=(6/2) kBT (solids)εavg=(5/2) kBT (diatomic molecules)lNote that if we have N particles:Eth=(3/2)N kBT =(3/2)nRT (monatomic gas)Eth=(6/2)N kBT =(6/2)nRT (solids)Eth=(5/2)N kBT =(5/2)nRT (diatomic molecules)Physics 207: Lecture 27, Pg 4Specific heatlMolar specific heats can be directly inferred from the thermal energy.Eth=(6/2)N kBT =(6/2)nRT (solid)ΔEth=(6/2)nRΔT=nCΔTC=3R (solid) lThe specific heat for a diatomic gas will be larger than the specific heat of a monatomic gas:Cdiatomic=Cmonatomic+RPage Physics 207 – Lecture 27Physics 207: Lecture 27, Pg 5Second Law and EntropylA perfume bottle breaks in the corner of a room. After some time, what would you expect?A)B)Physics 207: Lecture 27, Pg 6very unlikelyprobability=(1/2)NlThe probability for each particle to be on the left half is ½.Page Physics 207 – Lecture 27Physics 207: Lecture 27, Pg 7Second Law of thermodynamicslThe entropy of an isolated system never decreases. It can only increase, or in equilibrium, remain constant.lThe laws of probability dictate that a system will evolve towards the most probable and most random macroscopic statelThermal energy is spontaneously transferred from a hotter system to a colder system.Physics 207: Lecture 27, Pg 8Reversible vs IrreversiblelThe following conditions should be met to make a process perfectly reversible:1. Any mechanical interactions taking place in the process should be frictionless.2. Any thermal interactions taking place in the process should occur across infinitesimal temperature or pressure gradients (i.e. the system should always be close to equilibrium.)Page Physics 207 – Lecture 27Physics 207: Lecture 27, Pg 9Reversible vs IrreversiblelBased on the above comments, which of the following processes is not reversible?A. Lowering a frictionless piston in a cylinder by placing a bag of sand on top of the piston.B. Lifting the piston described in the previous statement by removing one tiny grain of sand at a time.Physics 207: Lecture 27, Pg 10Heat EngineslTurning heat into work: Industrial revolution.VolumePressureifPage Physics 207 – Lecture 27Physics 207: Lecture 27, Pg 11Key conceptslWork done by the system:Wsystem=-WexternallEnergy reservoir: An object that interacts with the system that is sufficiently large such that its temperature is almost constant.QH: The amount of heat transferred to/from hot reservoirQC: The amount of heat transferred to/from cold reservoirPhysics 207: Lecture 27, Pg 12Energy-transfer diagramHot reservoirCold reservoirQHQCWoutcyclic systemΔEsystem=0Wout=QH-QCPage Physics 207 – Lecture 27Physics 207: Lecture 27, Pg 13Thermal efficiencyFor practical reasons, we would like an engine to do the maximumamount of work with the minimum amount of fuel. We can measure the performance of a heat engine in terms of its thermalefficiencyη(lowercase Greek eta), defined asWe can also write the thermal efficiency asPhysics 207: Lecture 27, Pg 14lWhat is the largest thermal efficiency that a heat engine can have?A) η=2B) η=1C) η=1/2D) η=0lWhat is the lowest thermal efficiency that a heat engine can have?A) η=1/2B) η=0C) η=-1/2D) η=-1Page Physics 207 – Lecture 27Physics 207: Lecture 27, Pg 15RefrigeratorslDevices that uses work to transfer heat from a colder object to a hotter object.Hot reservoirCold reservoirQHWinWin+QC=QHK=QC/WinQCPhysics 207: Lecture 27, Pg 16Is perfect engine possible?Hot reservoirCold reservoirQH1WoutWinQH2QC=QCQHPage Physics 207 – Lecture 27Physics 207: Lecture 27, Pg 17Turbines: Brayton CyclePhysics 207: Lecture 27, Pg 18lWhich of the following processes would have the largest work output per cycle?VPVVPPA)B) C)Page Physics 207 – Lecture 27Physics 207: Lecture 27, Pg 19Internal combustion engine: gasoline engine(Adiabats)lA gasoline engine utilizes the Otto cycle, in which fuel and airare mixed before entering the combustion chamber and are then ignited by a spark plug.Otto CyclePhysics 207: Lecture 27, Pg 20The best thermal engine ever, the Carnot enginelA perfectly reversible engine (a Carnot engine) can be operated either as a heat engine or a refrigerator between the same two energy reservoirs, by reversing the cycle and with no other changes.Page Physics 207 – Lecture 27Physics 207: Lecture 27, Pg 21The Carnot EnginelAll real engines are less efficient than the Carnot engine because they operate irreversibly due to the path and friction as they complete a cycle in a brief time period.llCarnot showed that the Carnot showed that the thermal efficiency of a thermal efficiency of a Carnot engine is:Carnot engine is:hotcoldcycleCarnot
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