Lecture 14 Interaction of 2 systems at different temperatures Irreversible processes 2nd Law of Thermodynamics Chapter 19 Heat Engines and Refrigerators Thermal interactions T s change via collisions at boundary not mechanical interaction Etot E1i E2i constant with 3 3 E1i 2 n1 RT1i and E2i 2 n2 RT2i elastic collision total energy conserved energy transfer from faster atom to slower atom on average energy transferred from 1 to 2 T 1i T2i Equilibrium E1f N1 E1f E1f Etot N1 N1 N2 N1 N2 E E 2f N1 N2 tot N1 N2 Etot W 0 barrier does not move 1st law gives Q1 E1 E1f E1i Q2 E2 E2f E2i and Q1 Q2 energy conservation 2 systems reach common final T due to energy exchange via atomic collisions in reality via wall but still no mechanical interaction Example 2 0 g of helium at an initial temperature of 300 K interacts thermally with 8 0 g of oxygen at an initial temperature of 600 K a What is the initial thermal energy of each gas b What is the final thermal energy of each gas c How much heat is transferred and in which direction d What is the final temperature Irreversible processes heat not transferred cold to hot conserves energy reversible microscopic molecular motions irreversible macroscopic phenomena New law past vs future Statistics of Very Large Numbers small probability for 1Nto 10 increase especially if 1 20 net result of many collisions is to transfer energy from 1 to 2 equilibrium state is most probable 2nd Law of Thermodynamics negligible probability not impossible for atoms to spontaneously order more random arrangements state variable entropy probability for macroscopic state to occur measures disorder 2 systems with different T s lower entropy more order than order turns into disorder information lost system runs down vastly more random states laws of probability informally i heat transferred from hotter to colder formally entropy of isolated system never decreases can order by reaching from outside e g refrigerator for cold to hot informally ii irreversible evolution from less likely to more likely macroscopic state gives time direction entropy increases is future Chapter 19 physical principles for all heat engines transform heat energy into work and refrigerators uses work to move heat from cold to hot 2nd law limit on efficiency Carnot cycle Today general concepts of turning heat into work heat engines and refrigerators Heat Work thermodynamics transformation of energy e g heat into work obeys i 1st law energy conservation Eth W Q ii 2nd law heat flows from hotter to colder spontaneously Work done by system Ws vs work done on system by external force W heat and work are 2 ways to transfer energy to system equilibrium F gas F ext Ws W the area under the pV curve Ws 0 W 0 during expansion energy transferred out of system 1st law Q Ws Eth heat used to do work or stored as thermal Energy Transfer diagrams energy reservoir hot or cold much larger than system temperature does not change when heat transferred between it and system due to difference in temperatures QH C 0 heat transferred to from a hot cold reservoir Q QC in 1st law heat transferred from system 1st law Q Ws Eth refers to system Q QH QC Ws 0 Eth 0 steady state QH QC system provides route for energy transfer from hot to cold heat transferred from cold to hot 1st law not violated if QH QC but 2nd law does not allow spontaneous transfer Efficiency of Heat Work Work into heat 100 efficient e g warm up rocks from ocean by rubbing W Eth back into ocean Eth QC continue as long as there is motion Heat into Work isothermal expansion 100 efficient but one time process piston reaches end of cylinder practical device must return to initial state for continued use but 2nd law does not allow perfect engine 100 efficient asymmetry of 2 conversions similar to heat transfer Heat engines closed cycle device e g car engine p T inside cylinder repeated extracts heat combustion of fuel does useful work move pistons exhausts heat radiator all state variables return to initial once every cycle Eth net 0 over 1 full cycle 1st law Eth net Qnet Wout with Qnet QH QC energy conservation thermal efficiency 1 QC QH perfect engine 1 not possible must exhaust energy waste heat energy extracted from hot reservoir not transformed into work A Heat Engine Example useful work of lifting mass during isobaric expansion step e no net change in gas start lifting mass again heat engines require source and sink reservoirs not explicitly shown TH highest system temperature TC coldest
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