Final Exam. Locations by Lab Instructor. Carnot Cycle. Physics 220. Lecture 27

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1 Physics 220 Lecture 27 hermodynamics II Final Exam Dec :20 AM - 12: 20 PM Half is 3rd est plus half is omprehensive 2/3 questions hapt /3 questions hapt You can bring 3 crib sheets #2 pencil, calculator, & I.D. In three rooms by lab "PRAIE EXAM FOR HE FINAL" on the homework page. 1 Purdue University, Physics Locations by Lab Instructor HR Mandal, Nirajan Lin, zu-ging Jung, Yookyung L ervantes, Mayra Mukundan, Vineetha Li, Xin-A See Home Page For lab hours Idealized Heat Engine No Friction Reversible Process Isothermal Expansion Adiabatic Expansion Isothermal ompression Adiabatic ompression all at arnot ycle Lilly Setty, handan Shao, Siyi Zhang, Shunyuan Purdue University, Physics Q all at his is most efficient engine 4

2 Refrigerator ycle Run it backward ounter clockwise Push down when hot and pull up when cold Requires work in but heat flows from cold to hot Purdue University, Physics Refrigerator: oefficient of Performance he objective: remove heat from cold reservoir he cost: work 1st Law: = + Q oefficient of performance K r " Q / = Q / = Q /( - Q ) REFRIGERAOR Lecture 26 Purdue University, Physics Q Engines and Refrigerators HEA ENGINE REFRIGERAOR Ideal Efficiency For a arnot engine! and Q! Q System Q e = 1-Q / = 1 - / arnot engine most efficient since it operates across greatest difference for given and! System taken in closed cycle # $U system = 0! herefore, net heat absorbed = work done - Q = (engine) Q - = - (refrigerator) energy into blob = energy leaving blob Lecture 26 Purdue University, Physics K r " Q / = Q / For refrigerator: = Q /( - Q ) = /( ) 8

3 Entropy Early steam engine designers noticed a tradeoff between efficiency and robust performance arnot engine very efficient but ran in reverse (refrigerator) as easily, or not at all onduction opposite limit e = 0 as = 0 Key was the discovery of a new parameter S = Q/ S always increased overall and more S generated the more robust the behavior of engine Purdue University, Physics Real Engines For ideal arnot engine i.e. Greatest possible efficiency e = 1-Q / = 1 - / and / = Q / conserved All operating engines are less efficient and / < Q / Define Entropy S = Q/ S > S H hen S out of hot reservoir is less than S into cold reservoir. otal S increases 10 New oncept: Entropy (S) A measure of disorder increased probability A property of a system (just like P, V,, U) related to number of different states of system Examples of increasing entropy: ice cube melts gases expand into vacuum hange in entropy: $S = Q/ >0 if heat flows into system (Q>0) <0 if heat flows out of system (Q<0) 11 Entropy Question Some ice (-5 ) is used to cool a cup of water $S = Q/ hat happens to the entropy of the ice? A) Increase B) Same ) Decreases Heat enters ice: Q>0 hat happens to the entropy of the water? A) Increase B) Same ) Decreases Heat Leaves water: Q<0 hat happens to the total entropy (water+ice)? A) Increase B) Same ) Decreases $S = Q/ ice Q/ water 12

4 Second Law of hermodynamics he entropy change (Q/) of the system+ environment % 0 never < 0 order to disorder onsequences A disordered state cannot spontaneously transform into an ordered state Less probable state transforms to more probable State Large size of systems means robust change 13 Engines and the 2nd Law he objective: turn heat from hot reservoir into work he cost: waste heat 1st Law: -Q = Efficiency e " / =/ = 1-Q / $S = Q / - / % 0 herefore, Q / % / $S = 0 for arnot Q / = / for arnot herefore e = 1 - Q / & 1 - / e = 1 - / for arnot e = 1 is forbidden! e largest if << HEA ENGINE 14 Q Entropy and Disorder In thermal conductivity the same heat flows from hot to cold = Q = Q Hot S = Q/ > S H = Q/ MORE S ADDED O OLD HAN AKEN FROM HO OAL S INREASE Q A LO BRINGS ABOU MORE DISORDER HAN IAUSED A HIGH old Efficiency Never = 1 e = 1-Q / Q > 0 If e = 1 the = hat could then run a refrigerator he combination would lead to net flow of Q from cold to hot. HEA ENGINE REFRIGERAOR QH QH System H Q H Q 15 16

5 Entropy and probability otal probability of hot and cold reservoir is the product of the probability of the two P = P H X P Probability of a state proportional to the number of individual arrangements that make it up All in left = 1/16 More Uniform = 6/16 Purdue University, Physics Role of size of physical systems Instead of 4 particles use N A -- n X Instead of 2 boxes an almost infinite number Ratio of uniform distribution compared others approaches infinity Probabilities so overwhelming that system seems to always approach equilibrium System seeks most probable state S proportional to Log of P Adding S 1 + S 2 is like Multiplying P 1 X P 2 Q A LO BRINGS ABOU MORE probability HAN I takes from HIGH Higher overall probability is what system seeks Purdue University, Physics

6 Summary of oncepts First Law of thermodynamics: Energy onservation Q = $U + Heat Engines Efficiency = 1-Q / Refrigerators oefficient of Performance = Q /( - Q ) Entropy $S = Q/ 2 nd Law: Entropy always increases! arnot ycle: Reversible, Maximum Efficiency e = 1 c / h 21

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