Thermodynamics: Coefficient of Performance Equation for Temperature Calculation

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Homework Help Overview

The discussion revolves around the coefficient of performance (COP) of heat pumps in thermodynamics, specifically focusing on the relationship between indoor and outdoor temperatures. Participants are exploring how to calculate COP using temperature values without additional information on heat transfer quantities.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants inquire about the existence of a formula for COP based solely on temperatures. They discuss the ideal Carnot engine assumptions and how to derive COP from temperature values.

Discussion Status

Some participants have provided guidance on the theoretical framework for COP and its relationship to temperature. There is ongoing exploration of how to apply these concepts given limited information, with questions about the necessity of converting temperature units and the meaning of joules of heat in the context of the problem.

Contextual Notes

Participants are working with specific temperature values (indoor and outdoor) and are questioning the need for conversions to Kelvin for their calculations. There is a focus on understanding the implications of the COP being a unit-less ratio.

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Just a quick question. Is there a formula for the coefficient of performance equation for just temperatures. All I have is the outdoor and indoor temperauture. How would I approach that?
 
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name_ask17 said:
Just a quick question. Is there a formula for the coefficient of performance equation for just temperatures. All I have is the outdoor and indoor temperauture. How would I approach that?
Yes, there is such a formula. It generally assumes that the heat pump (or refrigerator) is an ideal Carnot engine (maximum efficiency -- no losses due to friction, etc.)

You should be able to find this set of equations in your textbook or coursework. There is one COP equation for heating (such as what is used by a heat pump) and another, similar equation for cooling (such as what is used by a refrigerator or air conditioner).

Or you can derive it yourself. For an ideal system, Qhot/Thot = Qcold/Tcold.
 
what is Q? how would i find that.
because in my problem, i literally only have Tc and Th. how do i do that?
 
name_ask17 said:
what is Q? how would i find that.
because in my problem, i literally only have Tc and Th. how do i do that?
Do you already have formulas for COP as a function of Qhot and Qcold?

Make your substitutions. For example, Qcold = TcoldQhot/Thot, for an ideal Carnot engine. Make a similar substitution for Qhot. :wink:
 
ok. this is my problem.
In a heat pump, heat from the outdoors at -8.00 deg c is transferred to a room at 22 deg c, energy being supplied by an electrical motor. How mnay joules of heat will be delivered to the room for each joule of electrical energy consumed, ideally?

when it asks for joules of heat, what specifically is this asking me to solve for? and if i use the equation you wrote above, do i have to convert it to kelvin or can i leave it as celsius?
 
name_ask17 said:
when it asks for joules of heat, what specifically is this asking me to solve for?
The coefficient of performance or COP of a heat pump is the ratio of the change in heat at the "output" (the heat reservoir of interest) to the supplied work.

So, the question is asking for just that. The question is asking for the COP of the system, assuming it is ideal.

And the question is asking for a ratio. So your answer is not going to be in units of Joules. Rather it's going to be a unit-less number. COP is a unit-less number.
and if i use the equation you wrote above, do i have to convert it to kelvin or can i leave it as celsius?
You absolutely have to convert to Kevlin!

You'll also at least have to find a formula for the COP in your textbook. I've given you enough information where you can convert the formula to be a function of Thot and Tcold instead of Qhot and Qcold. But you'll at least need to find a formula for your textbook or coursework that gives you the COP in terms of Qhot and Qcold.
 

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