Carnot Freezer Engine Efficiency Calculation

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Homework Help Overview

The discussion revolves around calculating the average power required for a Carnot freezer to maintain a constant temperature, given specific temperatures and a heat leak due to imperfect insulation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants express uncertainty about how to start the problem and whether they have sufficient formulas. Some suggest using the definition of power and the relationship between work and heat transfer in the context of a Carnot engine.

Discussion Status

Several participants have offered insights into the relationships between heat transfer and work in a Carnot freezer. There is a focus on determining the necessary heat removal and the work required to achieve that, with no explicit consensus reached yet.

Contextual Notes

Participants note the importance of the thermal coefficient and the need to relate the given temperatures and heat transfer rates to the work done by the motor. The discussion highlights the challenge of interpreting the problem with the provided information.

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Homework Statement


A Carnot freezer in a kitchen has constant temperature of 260k, while the air in the kitchen has a constant temperature of 300K. Suppose the insulation for the freezer is not perfect and energy is conducted into the freezer at a rate of .15 Watts. Determine the average power required for the freezer's motor to maintain the constant temperature in the freezer.


Homework Equations



Qc/Qh=Tc/Th for a Carnot engine

efficiency = (Th - Tc)/(Th)

Work = Qh-Qc

The Attempt at a Solution



I'm not really sure where to begin. It doesn't seem like I have enough formulas to tackle this problem.
 
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The definition of power might be useful
 
I know power = work/time. So .15J of heat per second are entering the freezer. For a carnot freezer, Work done = Th-Tc = 40J.
 
Last edited:
No one? :(
 
reb659 said:
I know power = work/time. So .15J of heat per second are entering the freezer. For a carnot freezer, Work done = Th-Tc = 40J.

Don't confuse T with Q.

If .15J are leaking into the freezer each second, what heat (Qc) needs to be
pumped out per second?
Now use your equations to find work done by the motor per second.
 
reb659 said:

Homework Statement


A Carnot freezer in a kitchen has constant temperature of 260k, while the air in the kitchen has a constant temperature of 300K. Suppose the insulation for the freezer is not perfect and energy is conducted into the freezer at a rate of .15 Watts. Determine the average power required for the freezer's motor to maintain the constant temperature in the freezer.


Homework Equations



Qc/Qh=Tc/Th for a Carnot engine

efficiency = (Th - Tc)/(Th)

Work = Qh-Qc

The Attempt at a Solution



I'm not really sure where to begin. It doesn't seem like I have enough formulas to tackle this problem.
Consider the amount of work required to remove a certain amount of heat from the cold reservoir to the hot reservoir. What is the relationship between W, Th and Tc for a Carnot refrigerator?

In this case, .15 Joules/sec have to be moved. The question asks you how much work (per second) you have to do in order to move that amount of heat.

AM
 
Your missing the Thermal Coefficient. Plug it in and you're there.
 
reb659 said:
Qc/Qh=Tc/Th for a Carnot engine

Work = Qh-Qc

We've effectively told you Qc.
You are given Tc and Th.

Use your first equation to find Qh,
then your second equation to find work.

This ain't rocket science, although it might be relevant to it:)
 

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