The new efficiency of the ideal engine rated at 50% is : 59%
Given data :
Inital exhaust temperature = 20ºC
Final exhaust temperature = - 30 ºC
The efficiency of an ideal engine can be calculated with the formula below
η = 1 - Texhaust / Tinput
Therefore :
Tinput = Texhaust / 1 - η ---- ( 2 )
where : Texhaust = 293 k , η = 0.50 ,
insert values into equation ( 2 )
Tinput = 293 / 1 - 0.50
= 586 k
The new efficiency of the ideal engine ;
η = 1 - T'exhaust / Tinput
= 1 - 243 / 586
= 1 - 0.41 = 59%
Hence we can conclude that the new efficieny is 59%
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