# Homework Help: (Thermodynamics) Engines Working in Pairs; Calculating Carnot effiency

1. Sep 26, 2008

### JerryG20

1. The problem statement, all variables and given/known data
At a steam power plant, steam engines work in pairs, the heat output of the first one being the approximate heat input of the second. The operating temperatures of the first are 720C and 428C, and of the second 417C and 260C.

If the heat of combustion of coal is 2.8 * 10^7, at what rate must coal be burned if the plant is to put out 950MW of power? Assume the efficiency of the engines is 65% of the ideal (Carnot) efficiency.

Water is used to cool the power plant. If the water temperature is allowed to increase by no more than 5.5C, estimate how much water must pass through the plant per hour.

2. Relevant equations
Carnot efficiency = 1 - TL/TH = 1 - QL/QH
Efficiency = W/QH

3. The attempt at a solution
I'm pretty lost on this one and am still working on the first part before trying to do the second part. For the first part, I believe you simply solve for "q" by equating [heat of combustion of coal] * [q] * [.65 * Carnot Efficiency] to [Power output]. Of course, the problem is solving for the Carnot efficiency.

I know the equations for Carnot efficiency, but I don't know quite how to apply them to 2 engines applied in series (I figured I could just multiply the individual efficiencies together but this gave me a wrong answer). So, I'm stuck trying to find the efficiency. I know that e = W/QH, and that QL for engine 1 can be used as the QH for engine 2, but I don't see how this can help any further as I don't have any way to calculate the work done.

Any help is appreciated. Thanks for reading.