Britannica Classics Check out these retro videos from Encyclopedia Britannica’s archives.The temperature at which the gases are exhausted from the engine ( T Cold ).The temperature of the combustion gases inside the engine ( T Hot ).In the case of an automobile, the two temperatures are: The temperature at which the low temperature reservoir operates ( T Cold ).The temperature at which the high temperature reservoir operates ( T Hot ).The Carnot Efficiency is the theoretical maximum efficiency one can get when the heat engine is operating between two temperatures: Note: Unlike the earlier equations, the positions of T cold and T hot are reversed. Η ′ ( % ) = 1 − T C o l d T H o t × 100 % MathTypeMTEF55+= feaagGart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8vrps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aacuaH3oaAgaqbamaabmaabaGaaiyjaaGaayjkaiaawMcaaiabg2da 9iaaigdacqGHsisldaWadaqaamaalaaabaGaamivamaaBaaaleaaca WGdbGaam4BaiaadYgacaWGKbaabeaaaOqaaiaadsfadaWgaaWcbaGa amisaiaad+gacaWG0baabeaaaaaakiaawUfacaGLDbaacqGHxdaTca aIXaGaaGimaiaaicdacaGGLaaaaa4EF7 So this equation, also called Carnot Efficiency, can be simplified as: The above equation is multiplied by 100 to express the efficiency as percent.įrench Engineer Sadi Carnot showed that the ratio of Q HighT to Q LowT must be the same as the ratio of temperatures of high temperature heat and the rejected low temperature heat. Η ′ ( % ) = 1 − Q C o l d Q H o t × 100 MathTypeMTEF55+= feaagGart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8vrps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aacuaH3oaAgaqbamaabmaabaGaaiyjaaGaayjkaiaawMcaaiabg2da 9iaaigdacqGHsisldaWadaqaamaalaaabaGaamyuamaaBaaaleaaca WGdbGaam4BaiaadYgacaWGKbaabeaaaOqaaiaadgfadaWgaaWcbaGa amisaiaad+gacaWG0baabeaaaaaakiaawUfacaGLDbaacqGHxdaTca aIXaGaaGimaiaaicdaaaa4E48 The symbol (Greek letter eta) is often used for efficiency this expression can be rewritten as: Where, Q Hot = Heat input at high temperature and Q Cold= Heat rejected at low temperature. Therefore, this expression becomes:Įfficiency= Q Hot -Q Cold Q Hot MathTypeMTEF55+= feaagGart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8vrps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aacaqGfbGaaeOzaiaabAgacaqGPbGaae4yaiaabMgacaqGLbGaaeOB aiaabogacaqG5bGaaeypamaalaaabaGaaeyuamaaBaaaleaacaqGib Gaae4BaiaabshaaeqaaOGaaeylaiaabccacaqGrbWaaSbaaSqaaiaa boeacaqGVbGaaeiBaiaabsgaaeqaaaGcbaGaaeyuamaaBaaaleaaca qGibGaae4Baiaabshaaeqaaaaaaaa5040
So work is equal to Heat at High temperature minus Heat rejected at Low temperature. A general expression for the efficiency of a heat engine can be written as:Įfficiency = Work HeatEnergy H o t feaagGart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8vrps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaqaafaaake aacaqGfbGaaeOzaiaabAgacaqGPbGaae4yaiaabMgacaqGLbGaaeOB aiaabogacaqG5bGaaeypamaalaaabaGaae4vaiaab+gacaqGYbGaae 4AaaqaaiaabIeacaqGLbGaaeyyaiaabshacaqGGaGaaeyraiaab6ga caqGLbGaaeOCaiaabEgacaqG5bWaaSbaaSqaaiaadIeacaWGVbGaam know that all the energy that is put into the engine has to come out either as work or waste heat.