Carnot freezer engine problem

In summary, the freezer's motor needs to pump out .15 Joules of heat per second in order to maintain the constant temperature.
  • #1
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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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  • #2
The definition of power might be useful
 
  • #3
I know power = work/time. So .15J of heat per second are entering the freezer. For a carnot freezer, Work done = Th-Tc = 40J.
 
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  • #4
No one? :(
 
  • #5
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.
 
  • #6
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
 
  • #7
Your missing the Thermal Coefficient. Plug it in and you're there.
 
  • #8
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:)
 

1. What is the Carnot freezer engine problem?

The Carnot freezer engine problem is a theoretical problem in thermodynamics that involves the efficiency of a refrigeration system. It was first proposed by French physicist Nicolas Léonard Sadi Carnot in 1824.

2. How does the Carnot freezer engine work?

The Carnot freezer engine works by using a cycle of compression and expansion of a refrigerant gas to remove heat from a cold space and transfer it to a hot space. This is known as the Carnot cycle and is the most efficient method of refrigeration.

3. What is the efficiency of the Carnot freezer engine?

The efficiency of the Carnot freezer engine is given by the Carnot efficiency formula, which is equal to (Th - Tc) / Th, where Th is the temperature of the hot reservoir and Tc is the temperature of the cold reservoir. This efficiency is the maximum possible efficiency for a refrigeration system.

4. What are the limitations of the Carnot freezer engine?

The Carnot freezer engine has several limitations, including the assumption of ideal gas behavior, reversible processes, and perfect insulation. In reality, these conditions are not achievable, making it impossible to reach the maximum efficiency predicted by the Carnot efficiency formula.

5. How is the Carnot freezer engine problem relevant today?

The Carnot freezer engine problem is still relevant today as it serves as a theoretical benchmark for comparing the efficiency of real-world refrigeration systems. It also highlights the importance of minimizing heat loss and maximizing efficiency in refrigeration technology, especially in the face of global warming and energy conservation efforts.

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