How Does a Heat Engine's Efficiency Impact Its Exhaust Heat Rate?

[mlostrac]

Homework Statement

A heat engine operates between 40°C and 380°C. Being a real engine, its
efficiency is only 60% of that theoretically possible for a Carnot engine at these
temperatures. If it absorbs heat at a rate of 60 kW, at what rate does it exhaust
heat?

Homework Equations

e = 1 - TL/TH --> Carnot Efficiency
e = 1 - QL/QH --> Efficiency

The Attempt at a Solution

1) First I changed the temperatures to Kelvins, then I calculated the Carnot efficiency:

e = 1 - (313/657)
= 1 - 0.48
= 0.52

2) Then I determined the actual efficiency to be:

0.52 x 0.60 = 0.31 or 31%

3) Finally I plugged in the efficiency in 2 to the 2nd equation above:

0.31 = 1 - (QL/60 kW)
60(0.31) = 60 - QL
18.72 = 60 - QL
QL = 41.3 kW

So therefore the engine exhausts heat at 41.3 kW or 41.3 kJ/s. I think I did this right, but I'm the type of guy who always manages to forget something or other.

Does this look right?

 

[rock.freak667]

Yes that looks right to me.