What is the minimum power required to operate the heat pump?

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Homework Help Overview

The discussion revolves around determining the minimum power required to operate a heat pump for heating a house, given specific temperature conditions and heat loss values. The subject area includes thermodynamics and heat transfer principles.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are examining the relationship between temperature ratios and power calculations, questioning the validity of the original poster's approach and the units involved in the calculations.

Discussion Status

There is an ongoing examination of the original calculations, with some participants suggesting that the dimensional analysis may be flawed. Clarifications regarding the use of units in the equations are being discussed, indicating a productive exploration of the problem.

Contextual Notes

Participants are addressing potential misunderstandings related to the application of equations and the importance of maintaining consistent units throughout the calculations.

swain1
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Homework Statement


It is proposed to heat a house using a heat pump operating between the house (27 degees) and the outside (-13 degrees). The heat loss from the house is 7kW. What is the minimum power required to operate the heat pump?

Homework Equations


The Attempt at a Solution


e=Th/(Th-Tc) =7.5
W=7000/7.5 =933 W

Just checking if this is correct or have I made a mistake. Thanks
 
Last edited:
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Since you start out with a dimensionless number, a ratio of temperatures, and equate that to some number of Watts, something is surely wrong. Maybe you just need to rewrite things to make it clear
 
I have moved the equation now. If you look at the question you will see that 7000 has units of watts. Is it wrong anyway?
 
swain1 said:
I have moved the equation now. If you look at the question you will see that 7000 has units of watts. Is it wrong anyway?

That looks better. It would be better still if you had units of W on the 7000.
 

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