# Cogeneration power cycle

## 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 $\dot{Q}_{out}$. 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$\cdot$h. If the cycle thermal efficiency is 40%, determine the (a) rate energy is added by heat transfer, $\dot{Q}_{in}$ in MW, (b) rate energy is discarded to the environment, in MW.

## Homework Equations

$W_{cycle} = Q_{in} - Q_{out}$
$\dot{Q}=\dot{W}$
$\eta = \frac{W_{cycle}}{Q_{in}}=\frac{Q_{in}-Q_{out}}{Q_{in}}$

## 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).

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Welcome to PF, treynolds147!

I think it's not the rate of heat transfer that is 80 MW.
It's the generated useful power $\dot W_{cycle}$ that is 80 MW.
With an $\eta$ of 40%, you should be able to find $\dot Q_{in}$.