# Thermodynamics and Steam Engine

1. Oct 21, 2009

### fallen186

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
WMax = $$\epsilon_{Max}*Q_{H}$$
W = QH-QC

3. 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?

2. Oct 21, 2009