Heat Pump Thermodynamics Question

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Discussion Overview

The discussion revolves around the thermodynamics of heat pumps, specifically focusing on the coefficient of performance (COP), energy balance, and the calculation of work input (W.in) required for heating a space. Participants explore theoretical and practical aspects of heat pump operation, including temperature changes and heat loss considerations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant outlines an approach to calculate the time required to raise the temperature of a house using a heat pump, referencing energy balance equations and COP.
  • Another participant suggests that the problem may lead to a differential equation, indicating a need for mathematical proficiency.
  • A different participant introduces the concept of minimum work required by a heat pump, referencing the Carnot efficiency and providing a formula for W based on heat transfer and temperature differences.
  • Some participants express frustration with educational limitations, noting that the scope of their class does not cover certain complexities, such as deriving W.in without given values.

Areas of Agreement / Disagreement

Participants generally express frustration with the limitations of their educational context, particularly regarding the depth of understanding expected. There is no consensus on the best approach to solve for W.in without additional information, and the discussion reflects a mix of theoretical exploration and practical concerns.

Contextual Notes

Participants acknowledge that the problem may exceed the scope of their current coursework, indicating potential limitations in their understanding of advanced thermodynamic concepts.

mcomputing
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I have a general question, it's not homework or anything, we are studying heat pumps and thermal efficiencies and COP. There's an example in my book that has a heat pump that is heating a house and it asks to find the minimum theoretical cost per day. Of course the solution and detailed steps are in my textbook.

However I was thinking what if I wanted to raise the temperature from any given T1 to T2 using a heat pump that gives me the COP and the heat loss or Q_loss and the mass of the house. I want to find how long it would take to raise the temperature from let's say 10 degrees Celsius to 22 degrees Celsius. I think I have an idea of how to go about solving such a problem.

Is the the process:

I have the energy balance equation which gives me sum(Q) = mC_v*delta(T)
I have a sum to be the Qin - Qloss = mC_v*delta(T). If I am given the Qloss and the mC_v and the Qin I can obviously solve for delta(T) and use that to find Tf if I am given a Ti.

Then I can use the COP equation of COP = Q.in/W.in to find Q.in. and Q.in would be equal to Qin/delta(t_sec).

Now my question is what if I wasn't given W.in for the heat pump, how would I be able to solve for it with my given information. Please advise. Thank you very much.
 
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Then you will have some sort of differential equation. How good is your math?
 
mcomputing said:
Now my question is what if I wasn't given W.in for the heat pump, how would I be able to solve for it with my given information.
The minimum work required by the heat pump is a function of the temperatures between which it is operating. For a Carnot heat pump:

COP = Qh/W = Qh/(Qh-Qc) = Th/(Th-Tc) so

W= Qh(Th-Tc)/Th = Qh(1-Tc/Th)

AM
 
Thanks for all your help. I was able to figure this out by asking my professor. He basically told me that not being given W.in is beyond the scope of the class I am taking. I think I was over thinking the question and imagining all possibilities.
 
mcomputing said:
Thanks for all your help. I was able to figure this out by asking my professor. He basically told me that not being given W.in is beyond the scope of the class I am taking. I think I was over thinking the question and imagining all possibilities.

I hate it when teachers say this.
 
khemist said:
I hate it when teachers say this.



This is a real-world problem (which I thought of and solved myself a while back) but he's too lazy to explain it to the student.That's the human mentality:

"If it don't make my paycheck bigger, I don't give a flying f***."
 

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