Question

a carnot engine has power output of 150 kilowatts engine operates between two reserviors at 20° Celsius and 500° celsius .How much energy is lost per hour in its exhaust.?

Answer 1

Answer:

3.41 × 10^8 J

Explanation:

ηc=Net Work Output / Heat Input= 1−TC / TH

TH=500∘C=773 K 

and a cold reservoir temperature :

 Tc=20∘C=293 K 

Then the efficiency of the engine is : 

ηc=1−293773=0.62/ηc=1−293773=0.62

(a) Given that the Carnot engine has a power output of P=150 kWP=150 kW

Hence the work it delivers per hour is : Net work output=150×103×3600=5.4×108 J/Net work output=150×103×3600=5.4×108 J

Then by equation (1) the heat input required per hour as :

0.62=5.4×108/Heat Inputor Heat Input=8.81×108 J0.62=5.4×108/Heat Inputor Heat Input=8.81×108 J

Thus the given Carnot engine takes 8.81×108 J/8.81×108 J of energy per hour.

(b) Next, we have to calculate the heat lost to the cold reservoir per hour.

Heat Input - Heat output=5.4×108 JorHeat Output =(8.81−5.4)×108=3.41×108 J Heat Input - Heat output=5.4×108 JorHeat Output =(8.81−5.4)×108=3.41×108 J

Thus 3.41×108 J3.41×108 J of energy is lost per hour to the exhaust.