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
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
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.