Physics
posted by Brianna .
You design an engine that takes in 1.5 x 10^4 J of heat at 650 K in each cycle and rejects heat at a temperature of 350 K. The engine completes 240 cycles in 1 minute. What is the theoretical maximum power output of your engine?
can you please also show what equations you use.

First get the maximum possible efficiency from the Carnot cycle formula
(Wout)/(Qin) max = 1  (Tin/Tout)
= 1  (350/650) = 46.2%
That efficiency applies to the work out per cycle or the average power divided by the heat transfer rate in.
You want power out, so compute the heat rate in. It is 4 cycles/s * 15,000 J = 60,000 W
Multiply that by the efficiency for the maximum power output. I get 27,692 W
Divide that by 746 W/Hp if you want horsepower.
Actual engines seldom exceed 2/3 of the Carnot efficiency, because the Carnot cycle is not practical for high speed engines.