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## Homework Statement

A cogeneration power plant is operating in a thermodynamic cycle at steady state. The plant provides electricity to a community at a rate of 80 MW. The energy discharged from the power plant by heat transfer is denoted by [itex]\dot{Q}_{out}[/itex]. Of this, 70 MW is provided to the community for water heating and the remainder is discarded to the environment without use. The electricity is valued at $0.08 kW[itex]\cdot[/itex]h. If the cycle thermal efficiency is 40%, determine the (a) rate energy is added by heat transfer, [itex]\dot{Q}_{in}[/itex] in MW, (b) rate energy is discarded to the environment, in MW.

## Homework Equations

[itex]W_{cycle} = Q_{in} - Q_{out}[/itex]

[itex]\dot{Q}=\dot{W}[/itex]

[itex]\eta = \frac{W_{cycle}}{Q_{in}}=\frac{Q_{in}-Q_{out}}{Q_{in}}[/itex]

## The Attempt at a Solution

I haven't the slightest idea how to even start this. There aren't even any worked examples in the book. I only know that the rate of heat transfer has to be equal to 80 MW (the power supplied by the plant).