Heat engine and Heat pump in combination

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Discussion Overview

The discussion revolves around the analysis of a combined heat engine and heat pump system, focusing on the application of the first and second laws of thermodynamics. Participants are attempting to solve a problem related to energy transfer and efficiency calculations, specifically aiming to compute the heat transfer rate (dQh/dt).

Discussion Character

  • Homework-related
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant presents an initial attempt at calculating the efficiency of the heat engine using the relationship QL/Qw1 = TL/Twaste and derives an efficiency of 0.93808.
  • Another participant suggests that the problem does not require efficiency but rather the computation of dQh/dt, proposing to write equations based on the first and second laws of thermodynamics.
  • There is a mention of needing to establish relationships between Qw1, Qw2, and a specified power output of 5 MW, indicating a system of equations to solve for Qh.
  • A participant expresses confusion regarding the number of equations needed for the first and second laws, indicating they only have the equation delta U = Q - W and a formula for entropy.
  • Another participant clarifies that there are two mechanisms (the heat engine and the heat pump), each requiring its own set of equations for the first and second laws.
  • There is a correction regarding the use of the equation dQ = TdS, which is noted as not being an expression of the second law but rather a formula for calculating entropy.
  • Participants discuss the implications of state functions in the context of the first law, emphasizing that internal energy does not change over a complete cycle.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specific equations needed or the correct approach to solving the problem. There is ongoing confusion and clarification regarding the application of thermodynamic laws to the heat engine and heat pump system.

Contextual Notes

Participants express uncertainty about the correct formulation of the first and second laws in relation to the combined system, and there are unresolved questions about the necessary equations and their application to the problem at hand.

canadiansmith
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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
 

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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.
 
rude man said:
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
 
canadiansmith said:
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.
 
Last edited:

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