Question

A heat engine uses a heat source at 540 ∘C and has an ideal (Carnot) efficiency of 25 % .To increase the ideal efficiency to 43 % , what must be the temperature of the heat source?

Answer 1

efficiency of ideal heat engine=1-(temperature of sink/temperature of source)

all the temperatures are taken in units of Kelvin.

temperature of heat source=273+540=813 K

here if temperature of sink is T K, then efficiency=1-(T/813)

hence 1-(T/813)=0.25

==>0.75=T/813

==>T=609.75 K

to improve efficiency to 0.43 , if new temprature of heat source is T1 ,

then 1-(609.75/T1)=0.43

==>0.57=609.75/T1

==>T1=1069.736 K=796.736 degree celcius