Physics 207 Lecture 27. Lecture 26. Chapters 18, entropy and second law of thermodynamics Chapter 19, heat engines and refrigerators
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1 Goals: Lecture 26 Chapters 18, entropy and second law of thermodynamics Chapter 19, heat engines and refrigerators Reading assignment for Wednesday: Chapter 20. Physics 207: Lecture 27, Pg 1 Entropy A perfume bottle breaks in the corner of a room. After some time, what would you expect? A) B) Physics 207: Lecture 27, Pg 2
2 very unlikely The probability for each particle to be on the left half is ½. probability=(1/2) N Physics 207: Lecture 27, Pg 3 Second Law of thermodynamics The entropy of an isolated system never decreases. It can only increase, or in equilibrium, remain constant. The laws of probability dictate that a system will evolve towards the most probable and most random macroscopic state Thermal energy is spontaneously transferred from a hotter system to a colder system. Physics 207: Lecture 27, Pg 4
3 Reversible vs Irreversible The 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.) Physics 207: Lecture 27, Pg 5 Reversible vs Irreversible Based 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 6
4 Heat Engines Turning heat into work: Industrial revolution. Pressure f i Volume Physics 207: Lecture 27, Pg 7 Work done by the system: Key concepts W system =-W external Energy reservoir: An object that interacts with the system, that is sufficiently large such that its temperature is almost constant. Q H : The amount of heat transferred to/from hot reservoir Q C : The amount of heat transferred to/from cold reservoir Physics 207: Lecture 27, Pg 8
5 Energy-transfer diagram Hot reservoir cyclic system E system =0 Q H W out W out =Q H -Q C Q C Cold reservoir Physics 207: Lecture 27, Pg 9 Thermal efficiency For practical reasons, we would like an engine to do the maximum amount of work with the minimum amount of fuel. We can measure the performance of a heat engine in terms of its thermal efficiency (lowercase Greek eta), defined as We can also write the thermal efficiency as Physics 207: Lecture 27, Pg 10
6 What is the largest thermal efficiency that a heat engine can have? A) =2 B) =1 C) =1/2 D) =0 What is the lowest thermal efficiency that a heat engine can have? A) =1/2 B) =0 C) =-1/2 D) =-1 Physics 207: Lecture 27, Pg 11 Refrigerators Devices that uses work to transfer heat from a colder object to a hotter object. Hot reservoir Q H W in +Q C =Q H W in QC K=Q C /W in Cold reservoir Physics 207: Lecture 27, Pg 12
7 Is perfect engine possible? Hot reservoir Q H1 Wout Win Q H2 Q C = Q H Q C Cold reservoir Physics 207: Lecture 27, Pg 13 Turbines: Brayton Cycle Physics 207: Lecture 27, Pg 14
8 The best thermal engine ever, the Carnot engine A 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. A Carnot cycle for a gas engine consists of two isothermal processes and two adiabatic processes A Carnot engine has max. thermal efficiency, compared with any other engine operating between T H and T C η Carnot = 1 T T Cold A Carnot refrigerator has a maximum coefficient of performance, compared with any other refrigerator operating between T H and T C. Hot K Carnot = TCold T T Hot Physics 207: Lecture 27, Pg 15 Cold The Carnot Engine Carnot showed that the thermal efficiency of a Carnot engine is: η Carnot cycle =1 T T cold hot All 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. Physics 207: Lecture 27, Pg 16
The need for something else: Entropy
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