# Heat engine and Heat pump in combination

Question is attached

I have spent a great deal of time on this problem and I am hoping someone can help me out.
My attempt at problem.

first for the heat engine
QL/Qw1 = TL/Twaste
so efficiency = 1- Tl/Twaste
efficiency = 0.93808
and I know that efficiency = Wout/ Qw1

This is as far as i got for the heat engine...

For Heat pump
i found cop = TH/(TH-TL) = 4.23

## Answers and Replies

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rude man
Homework Helper
Gold Member
Never mind efficiency. The problem doesn't ask for efficiency. It only wants you to compute dQh/dt.

ANYWAY ...

write the equations for the 1st and 2nd laws. That's 4 equations.

Then write the relationship between Qw1, Qw2 and 5 MW.

5 equations, 5 unknowns. Away you go. Solve for Qh.

(Note - the 1st and 2nd laws are usually written in terms of energy rather than power. Don't let that slow you down. Just pretend it's energy for 1 second, which of course is 1 J/s = 1 W.

Never mind efficiency. The problem doesn't ask for efficiency. It only wants you to compute dQh/dt.

ANYWAY ...

write the equations for the 1st and 2nd laws. That's 4 equations.

Then write the relationship between Qw1, Qw2 and 5 MW.

5 equations, 5 unknowns. Away you go. Solve for Qh.

(Note - the 1st and 2nd laws are usually written in terms of energy rather than power. Don't let that slow you down. Just pretend it's energy for 1 second, which of course is 1 J/s = 1 W.
I am still a little confused. There are 2 equations for both first and second law?
i only have delta U = Q-W
and Q = integral of TodeltaS

rude man
Homework Helper
Gold Member
I am still a little confused. There are 2 equations for both first and second law?
i only have delta U = Q-W
and Q = integral of TodeltaS
Yes, but you have two mechanisms, the heat engine and the heat pump. Each has its own
1st & 2nd law equations.

BTW dQ = TdS is not an expression of the second law. It's just a formula to calculate entropy. What you need is an expression reflective of the fact that entropy is unchanged in a reversible cycle.

As for the 1st law, you are right, but what can you say about Qw1, QL, Qw2, QH and W? Remember that U is a state function so over a cycle it doesn't change either, reversible or not.

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