Physics 121 April 29 2008 The Second Law of Thermodynamics http www horizons uc edu MasterJuly1998 oncampus htm Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 121 April 29 2008 Course Information Topics to be discussed today The Second Law of Thermodynamics Applications of the Second Law the Carnot Engine Entropy The End Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 121 April 29 2008 Homework set 10 is now available and is due on Wednesday evening April 30 at 11 30 pm Exam 3 will be returned in workshops Any complaints about Exam 3 must be addressed by me please write down why you feel the exam was not graded properly and hand it to me before next Monday May 5 I will do the re grading on Tuesday morning May 6 I have distributed information about the score you need to obtain on the final exam to get a C a B and an A in this course Frank L H Wolfs Department of Physics and Astronomy University of Rochester 1 Physics 121 Grade Requirements Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 121 Final Exam Details The final exam will be held on Thursday May 8 between 4 pm and 7 pm in Hubbell The final exam will cover all the material discussed in the course there will be NO particular focus on thermodynamics NOTE no error analysis Extra office hours of the TAs and me will be announced via email later this week The formula sheet to be attached to the final exam will be distributed via email by the end of the weekend and will also be available on the WEB Please use all the resources at your disposal to prepare for the exam e g the detailed solutions of previous exams the homework assignments the study guide etc The final exam grades will be distributed via email on Monday May 12 Frank L H Wolfs Department of Physics and Astronomy University of Rochester Second law of thermodynamics There are several different forms of the second law of thermodynamics It is not possible to completely change heat into work with no other change taking place Heat flows naturally from a hot object to a cold object heat will not flow spontaneously from a cold object to a hot object Many naturally processes do not violate conservation of energy when executed in reverse but would violate the second law Frank L H Wolfs Department of Physics and Astronomy University of Rochester 2 Second law of thermodynamics Heat engines Most engines rely on a temperature difference to operate Let s understand why The steam pushes the piston to the right and does work on the piston Win nRTin 1 Vin Vout To remove the steam the piston has to do work on the steam Wout nRTout 1 Vout Vin If T in Tout Win Wout 0 no net work is done In order to do work T in Tout and we must thus cool the steam before compression starts Frank L H Wolfs Department of Physics and Astronomy University of Rochester Second law of thermodynamics Heat engines The efficiency of an engine is defined as the ratio of the heat extracted from the hot reservoir and the work done Efficiency W QH The work done and the heat extracted are usually measured per engine cycle Because of the second law no engine can have a 100 efficiency Note the cost of operation does not only depend on the cost of maintaining the high temperature reservoir but may also include the cost of maintaining the cold temperature reservoir Frank L H Wolfs Department of Physics and Astronomy University of Rochester Second law of thermodynamics Heat pumps In many cases heat engines the conversion of flow of heat to work is the primary purpose of the engine e g the car engine In many other applications heat pumps work is converted to a flow of heat e g air conditioning The performance of a heat pump is usually specified by providing the coefficient of performance K K QL W Frank L H Wolfs Department of Physics and Astronomy University of Rochester 3 Second law of thermodynamics Heat pumps Note you can not cool your house by opening the door of your refrigerator Frank L H Wolfs Department of Physics and Astronomy University of Rochester Second law of thermodynamics Heat pumps Note You usually pay for the work done but not for the heat extracted from the outside You can thus get more energy than what you pay for Frank L H Wolfs Department of Physics and Astronomy University of Rochester Second law of thermodynamics Heat pumps http irc nrc cnrc gc ca cbd cbd195e html Heat pumps The heat capacity increases with increasing outside temperature Additional heaters may required in colder climates be The heat capacity can also be increased by changing the source of heat from the air to the ground http www bchydro com powersmart elibrary elibrary685 html Frank L H Wolfs Department of Physics and Astronomy University of Rochester 4 Second law of thermodynamics Heat pumps Heat pumps Heaters in the winter take heat from the outside to the inside Air conditioners in the summer take heat from the inside to the outside Frank L H Wolfs Department of Physics and Astronomy University of Rochester Second Law of Thermodynamics The Carnot Cycle A perfect engine used to determine the limits on efficiency Frank L H Wolfs Department of Physics and Astronomy University of Rochester Second Law of Thermodynamics The Carnot Cycle Step 1 a to b The gas is in contact with a heat bath at temperature TH and weight is removed from the piston The gas expands while maintaining a constant temperature the change in the internal energy is thus equal to 0 J Using the first law of thermodynamics we see that Q H WH n R T H ln Frank L H Wolfs Vb Va Department of Physics and Astronomy University of Rochester 5 Second Law of Thermodynamics The Carnot Cycle Step 2 b to c The gas is isolated from the environment and some more weight is removed from the piston The gas expands and during the adiabatic expansion the temperature of the gas will decrease For adiabatic expansion pV is constant and we can thus related state b to state c THVb 1 TCVc 1 Frank L H Wolfs Department of Physics and Astronomy University of Rochester Second Law of Thermodynamics The Carnot Cycle Step 3 c to d The gas is in contact with a heat bath at temperature T C and weight is added to the piston The gas is compressed while maintaining a constant temperature the change in the internal energy is thus equal to 0 J Using the first law of thermodynamics we see that Q c Wc n R TC ln Frank L H Wolfs Vc Vd Department of Physics and Astronomy University of Rochester Second Law of