Thermodynamics and Steam Engine

[fallen186]

Homework Statement

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

Homework Equations

W_Max = $$\epsilon_{Max}*Q_{H}$$
W = Q_H-Q_C

The Attempt at a Solution

$$W = \frac{1}{2}*\epsilon_{Max}*Q_{H}$$

$$\frac{2W}{\epsilon_{Max}} = Q_{H}$$

$$W = Q_{H} - Q_{C}$$

$$W = \frac{2W}{\epsilon_{Max}} - Q_{C}$$

$$\epsilon_{Max} *W = 2W - \epsilon_{Max} * Q_{C}$$

$$\epsilon_{Max} *W - 2W= - \epsilon_{Max} * Q_{C}$$

$$W(\epsilon_{Max} - 2) = - \epsilon_{Max} * Q_{C}$$

$$\frac{W(\epsilon_{Max} - 2)}{- \epsilon_{Max}} = Q_{C}$$

$$Answer = \frac{2W (1-\frac{\epsilon_{Max}}{2})}{ \epsilon_{Max}}$$

Where did i go wrong?

 

[Gear300]

What is the given answer?

 

[Andrew Mason]

Maybe they want you to express the maximum efficiency in terms of temperatures Tc and Th.

AM