Calculating Heat Discharge in a Steam Engine: Efficiency and Work Rate Analysis

[kasse]

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

e_max = W/Q_H (Carnot)

e_max = W/2Q_H

--> Q_H = W/e_max

Wrong answer. What is my mistake?

 

[Jupiter6]

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

e_max = W/Q_H (Carnot)

e_max = W/2Q_H

--> Q_H = W/e_max

Wrong answer. What is my mistake?

Theoretical max would be equal to 1, 50% would be the actual efficiency = .5 =W/Q_H=1/2. Heat discharged would be Q_L which equals Q_H-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-T_L/T_H.