Lecture 16 Maximum efficiency for a perfectly reversible engine conditions for perfectly reversible engine efficiency for Carnot cycle Reversible Engine What s most efficient heat engine refrigerator operating between hot and cold reservoirs at temperatures TC and TH i e 0 99 allowed or is there an max for given TH C related refrigerator is heat engine running backwards perfectly reversible engine device can be operated between same two reservoirs with same energy transfers only direction reversed cannot be Brayton cycle engine need to change temperatures of reservoirs use heat engine to drive refrigerator no net heat transfer Limits of efficiency I Proof by Contradiction II suppose heat engine with more efficiency than perfectly reversible for same Wout new heat engine exhausts needs less heat to from cold hot reservoir Wout QH and Wout QH QC use it to operate perfectly reversible refrigerator engine extracts less heat from hot reservoir than refrigerator exhausts heat transferred from cold to hot without outside assistance forbidden by 2nd law Limits of efficiency II 2nd law informal statements 5 6 no heat engine more efficient than perfectly reversible engine operating between two reservoirs no refrigerator has larger coefficient of performance Conditions for reversible engine Carnot so far exists next design it and calculate efficiency max heat transfer thru an finite temperature difference is irreversible must use i frictionless no heat transfer Q 0 and ii heat transfer in isothermal processes Eth 0 Carnot engine maximum and K exchange of energy in mechanical interactions pushes on piston reversible if i Wout Win and ii system returns to initial T only if motion is frictionless reversible if heat transferred infinitely slowly infinitesimal temperature difference in isothermal process Carnot cycle enough to determine efficiency of Carnot engine using ideal gas ideal gas cycle 2 isothermal Eth 0 and 2 adiabatic processes Q 0 slow isothermal compression 1 2 Q12 removed adiabatic compression 2 3 till TH isothermal expansion 3 4 Q34 transferred adiabatic expansion 4 1 to TC work during 4 processes heat transferred during 2 isothermal Find 2 Q s for thermal efficiency 1 V1 V2 Q12 nRTC ln V4 Q34 nRTH ln V3 Carnot 1 QC QH QC Q12 TC ln V1 V2 TH ln V4 V3 Maximum Carnot efficiency Using T V 1 constant for adiabatic V1 V2 V4 V3 Similarly for refrigerator Earlier 1 not allowed by 2nd law but 0 99 is Next can t be more efficient than perfectly reversible Now result for Carnot thermal efficiency 2nd law informal statements 7 8 no heat engine refrigerator TC TC can exceed Carnot 1 TH and KCarnot TH TC high efficiency requires T T difficult in practice 1 expected from energy conservation vs limits from 2nd law H C Example A Carnot engine operating between energy reservoirs at temperatures 300 K and 500 K produces a power output of 1000 W What are a the thermal efficiency of this engine b the rate of heat input in W and c the rate of heat output in W Electricity chapters 26 32 going beyond Newton s laws electricity and magnetism connected PHY 270 microscopic level relation of charges to atoms molecules atoms neutral made of charged particles electrons and protons can be separated and moved atoms held by electric force macroscopic mechanical forces due to electric at atomic level this week chapter 26 Electric Charges and Forces charge model to describe basic electric phenomena how charges behave in insulators and conductors calculate forces using Coulomb s law field model review properties of vectors charges at rest and in motion currents less experience e g don t see movement of charges new concept of field to describe interactions macroscopic description Charge Model I Rubbing objects causes forces e g plastic comb picks up paper shock on touching metal doorknob after walking across carpet understand electric phenomena in terms of charges and forces between them without reference to atoms electrons experiments with rubbing of plastic glass rods on wool silk no forces originally neutral both attractive and repulsive cf gravity long range forces like gravity after rubbing charging attractive force between charged and neutral object test for object being charged picks up paper Postulates of Charge Model Rubbing adds removes charge larger for more vigorous Two like charges repel two opposite charges attract Neutral objects equal mixture of 2 charges rubbing separates Charge can be transferred by contact removing charge discharging Conductors charges move easily e g metal vs Insulators charges remain fixed e g plastic both can be charged Two kinds of charges plastic and glass others can be charged too positive and negative Force between charges is long range increases with quantity of charge decreases with distance more experiments with metal spheres
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