Lecture 12 _Nhietdonghco_Heat Engine

Heat engines, Heat pumbs, Refrigerators

LECTURE HEAT ENGINES, HEAT PUMPS, REFRIGERATORS 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 a Heat Engine The Efficiency of an Engine e  Work_ done_ by _ the _ engine W'  Heat _ received_ from_ hot _ reservoir Qh Engine operates in a cycle process, the change in internal energy is 0: U  Qh  Qc  W  Work done by the engine: ' W'  W  Qh  Qc  Qh  Qc W' Qh  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'  Qh  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: QAB  nRTh ln( BC : adiabatic: QBC  CD : isothermal: QCD  nRTc ln( DA : adiabatic: QDA  V Qh  QAB  nRTh ln( B ) VA V Q'c  QCD  nRTc ln( C ) VD V Tc ln( C ) Q' VD e  1 c  1 V Qh Th ln( B ) VA VB )0 VA System received heat VD )  System released VC Heat 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  TcVC 1 DA : adiabatic: TV 1  const VB VC  VA VD Th VA 1  TcVD 1 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 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(coolingmode)  heat _ received_ from_ cold _ reservoir Qc  Work_ done_ on _ the _ refrigerator W U  Qh  Qc  W  W  Qh  Qc  Q'h Qc Qc COP(coolingmode)  Q'h Qc Tc Carnot_ cycle: COP(coolingmode)  Th  Tc Heat Pump heat _ delivered_ to _ hot _ reservoir Q'h COP(heatingmode)   Work_ done_ on _ the _ heatpump W U  Qh  Qc  W  W  Qh  Qc  Q'h Qc Q'h COP(heatingmode)  Q'h Qc Th Carnot_ cycle: COP(heatingmode)  Th  Tc SUMMARY Heatengine efficiency W' Qh  Q'c Q'c e   1 Qh Qh Qh Qc Qc Re frigerator COP(coolingmode)   W Q'h Qc Heatpump W  Q'h Qc Q'h Q'h COP(heatingmode)   W Q'h Qc 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: QAB  BC : isovolumetric : QBC  nCV (TC  TB )  CD : adiabatic: QCD  DA : isovolumetric : QDA  nCV (TA  TD )  Qh  QBC  nCV (TC  TB ) Q'c  QDA  nCV (TD  TA ) Q' T T e  1 c  1 D A Qh TC  TB AB: adiabatic: TV 1  const TAV1 1  TBV2 1 CD : adiabatic: TV 1  const TDV1 1  TCV2 1 V1 1 TB TC TC  TB     1 T TD TD  TA V2 A  V2  Q'c e  1     Qh  V1   1 ... is done by the engine, • (3) energy is expelled by heat to a lowertemperature reservoir The Efficiency of a Heat Engine The Efficiency of an Engine e  Work_ done_ by _ the _ engine W'  Heat...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... (B)How much work does this engine in one cycle? Q'c 1.5 103 e  1  1  25% Qh 10 ' W'  Qh  Qc  (2 10 )  (1.5 10 )  0.5 10 J 3 The Carnot Engine • The engine operates in a cyclic