# Steam engine problem

## Homework Statement

If a steam engine operates at half of its theoretical maximum efficiency, and does work at a rate of W J/s, calculate how much heat is discharged per second.

## The Attempt at a Solution

emax = W/QH (Carnot)

emax = W/2QH

--> QH = W/emax

Wrong answer. What is my mistake?

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## Homework Statement

If a steam engine operates at half of its theoretical maximum efficiency, and does work at a rate of W J/s, calculate how much heat is discharged per second.

## The Attempt at a Solution

emax = W/QH (Carnot)

emax = W/2QH

--> QH = W/emax

Wrong answer. What is my mistake?
Theoretical max would be equal to 1, 50% would be the actual efficiency = .5 =W/QH=1/2. Heat discharged would be QL which equals QH-W. If the engine is operating at 50% efficiency, half the heat input will go to shaft work, the other half will be discharged. So this engine would discharge 1 J/s. BTW, theoretical max. for a heat engine is 1-TL/TH.