Thermodynamics filled in class notes_Part_25

# Thermodynamics filled in class notes_Part_25 - 2.7 OTTO 57...

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Unformatted text preview: 2.7. OTTO 57 The thermal efficiency is found as follows: Î· = w net q H , (2.354) = q H âˆ’ q L q H , (2.355) = 1 âˆ’ q L q H , (2.356) = 1 âˆ’ c v ( T 4 âˆ’ T 1 ) c v ( T 3 âˆ’ T 2 ) , (2.357) = 1 âˆ’ T 4 âˆ’ T 1 T 3 âˆ’ T 2 , (2.358) = 1 âˆ’ T 1 parenleftBig T 4 T 1 âˆ’ 1 parenrightBig T 2 parenleftBig T 3 T 2 âˆ’ 1 parenrightBig . (2.359) Now one also has the isentropic relations: T 2 T 1 = parenleftbigg V 1 V 2 parenrightbigg k âˆ’ 1 , (2.360) T 3 T 4 = parenleftbigg V 4 V 3 parenrightbigg k âˆ’ 1 . (2.361) But V 4 = V 1 and V 2 = V 3 , so T 3 T 4 = parenleftbigg V 1 V 2 parenrightbigg k âˆ’ 1 = T 2 T 1 . (2.362) Cross multiplying the temperatures, one finds T 3 T 2 = T 4 T 1 . (2.363) Thus the thermal efficiency reduces to Î· = 1 âˆ’ T 1 T 2 . (2.364) In terms of the compression ratio r v = V 1 V 2 , one has Î· = 1 âˆ’ r 1 âˆ’ k v = 1 âˆ’ 1 r k âˆ’ 1 v . (2.365) Note if the compression ratio increases, the thermal efficiency increases. High compression ratios introduce detonation in the fuel air mixture. This induces strong pressure waves inratios introduce detonation in the fuel air mixture....
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Thermodynamics filled in class notes_Part_25 - 2.7 OTTO 57...

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