Lecture 9 heat engine

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CHAPTER 22 HEAT ENGINES, ENTROPY, AND THE SECOND LAW OF THERMODYNAMICS Lecturer: Tran Thi Ngoc Dung heat engine • A heat engine is a device that takes in energy by heat and, operating in a cyclic process, expels a fraction of that energy by means of work • A heat engine carries some working substance through a cyclic process during which • (1) the working substance absorbs energy by heat from a high-temperature energy reservoir, • (2) work is done by the engine, • (3) energy is expelled by heat to a lowertemperature reservoir The Efficiency of an Engine The Efficiency of an Engine e  Work_ done _ by _ the _ engine W'  Heat _ received_ from_ hot _ reservoir Q h Engine operates in a cycle process, the change in internal energy is 0: U  Qh  Qc  W  Work done by the engine: W '   W  Q h  Qc  ' Q h  Qc W ' Q h  Q 'c Q 'c e   1 Qh Qh Qh Example • An engine transfers 2.00 x 103 J of energy from a hot reservoir during a cycle and transfers 1.50 x 103 J as exhaust to a cold reservoir (A)Find the efficiency of the engine (B)How much work does this engine in one cycle? Q 'c 1.5  103 e  1  1  25% Qh  10 W'  ' Q h  Qc  (2  10 )  (1.5  10 )  0.5  10 J 3 The Carnot Engine • The engine operates in a cyclic process consisting of isothermal processes and adiabatic processes AB : isothermal : Q AB  nRTh ln( VB )0 VA BC : adiabatic : Q BC  CD : isothermal : Q CD  nRTc ln( DA : adiabatic : Q DA  Q h  Q AB  nRTh ln( VB ) VA Q'c  Q CD  nRTc ln( VC ) VD VC ) Q'c VD e  1  1 V Qh Th ln( B ) VA Tc ln( VD )0 VC The Carnot Engine (cont.) VC ) Q'c VD e  1  1 V Qh Th ln( B ) VA Tc ln( BC : adiabatic : TV  1  const Th VB 1  Tc VC 1 DA : adiabatic : TV  1  const Th VA 1  Tc VD 1 VB VC  VA VD Tc e  1 Th Carnot Cycle In process D -A , (Active Fig 22.9d), the base of the cylinder is replaced by a nonconducting wall and the gas is compressed adiabatically The temperature of the gas increases to Th, and the work done by the piston on the gas is WDA In process C S D (Active Fig 22.9c), the gas is placed in thermal contact with an energy reservoir at temperature Tc and is compressed isothermally at temperature Tc During this time, the gas expels energy |Qc| to the reservoir and the work done by the piston on the gas is WCD Process A B is an isothermal expansion at temperature Th The gas is placed in thermal contact with an energy reservoir at temperature Th During the expansion, the gas absorbs energy |Qh| from the reservoir through the base of the cylinder and does work WAB in raising the piston In process B C (Active Fig 22.9b), the base of the cylinder is replaced by a thermally nonconducting wall and the gas expands adiabatically; that is, no energy enters or leaves the system by heat During the expansion, the temperature of the gas decreases from Th to Tc and the gas does work WBC in raising the piston 22.2 Heat Pumps and Refrigerators In a refrigerator or a heat pump, the engine takes in energy |Qc| from a cold reservoir and expels energy |Qh| to a hot reservoir (Active Fig 22.4), which can be accomplished only if work is done on the engine Refrigerator The effectiveness of a heat pump /refrigerators is described in terms of a number called the coefficient of performance COP(cooling mod e)  heat _ received _ from _ cold _ reservoir Q c  Work _ done _ on _ the _ refrigerator W U  Q h  Q c  W  W   Q h  Q c  Q 'h  Q c Qc COP(cooling mod e)  Q 'h  Q c Tc Carnot _ cycle : COP(cooling mod e)  Th  Tc Heat Pump COP(heating mod e)  heat _ delivered _ to _ hot _ reservoir Q'h  Work _ done _ on _ the _ refrigerator W U  Q h  Q c  W  W   Q h  Q c  Q 'h  Q c Q 'h COP(heating mod e)  Q 'h  Q c Carnot _ cycle : COP(heating mod e)  Th Th  Tc Example 22.5 Efficiency of the Otto Cycle Find the thermal efficiency of an engine operating in an idealized Otto cycle Treat the working substance as an ideal gas AB : adiabatic : Q AB  BC : isovolumetric : Q BC  nC V (TC  TB )  CD : adiabatic : QCD  DA : isovolumetric : Q DA  nC V (TA  TD )  Q h  Q BC  nC V (TC  TB ) Q'c  Q DA  nC V (TD  TA ) Q' T  TA e  1 c  1 D Qh TC  TB AB : adiabatic : TV  1  const TA V1 1  TBV2 1 CD : adiabatic : TV  1  const TD V1 1  TC V2 1 V1 1 TB TC TC  TB     1 TA TD TD  TA V2  V2  Q'c e  1     Qh  V1   1 .. .heat engine • A heat engine is a device that takes in energy by heat and, operating in a cyclic process, expels a fraction of that energy by means of work • A heat engine carries... absorbs energy by heat from a high-temperature energy reservoir, • (2) work is done by the engine, • (3) energy is expelled by heat to a lowertemperature reservoir The Efficiency of an Engine The Efficiency... The Efficiency of an Engine The Efficiency of an Engine e  Work_ done _ by _ the _ engine W''  Heat _ received_ from_ hot _ reservoir Q h Engine operates in a cycle process, the change in internal