Carnot Engine refrigerator temp

In summary, a Carnot refrigerator takes in 18 J of heat every second and expels 20 J into a room at a temperature of 23oC. The coefficient of performance is 18/2=6.62, meaning that the refrigerator is able to cool off the cold reservoir by 6.62oC.
  • #1
physgrl
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Homework Statement



A Carnot engine is operated as a refrigerator, taking in 18 J of heat every second and expelling 20 J into a 23oC room. What is the temperature inside the refrigerator?

a. 15.4oC
b. 3.33oC
c. -6.62 oC
d. -15.4 oC

Homework Equations



e=1-T(cold)/T(hot)
U=Q-W

The Attempt at a Solution



I have no idea how to approach this problem :s
 
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  • #2
First determine how much heat is transferred to or from the hot and cold reservoirs and how much work is needed to do that.
 
  • #3
isnt the heat just 18 and the work 20?
 
  • #4
Nope. For one thing, there are two heat transfers, heat absorbed and heat expelled by the engine/refrigerator. There's probably a picture in your textbook illustrating the flow of energy through a Carnot refrigerator.
 
  • #5
how can the efficiency be more than one?? because its receiving 18 and giving out 20?
 
  • #6
how can i get the heat?
 
  • #7
does it make sense to say that Q(absorbed)-20J=Q(given out)+18J??
 
  • #8
No, that doesn't make sense.

Forget the refrigerator for a second. How does a heat engine work? I'm not interested in details. I'm looking for a general description.
 
  • #9
Ok...i don't understand them very well but i know that they turn heat into work, that some heat is lost, and that the efficiency measures how much heat actually becomes work.
 
  • #10
Yes, that's perfect. A heat engine absorbs heat QH from a hot reservoir. Some of it is turned into work W. The rest of it QC gets expelled to a cold reservoir. This fact is expressed in the equation QH=W+QC.

A Carnot refrigerator is a heat engine that runs backward. Instead of absorbing heat from the hot reservoir, it expels heat into the hot reservoir. Instead of expelling heat to the cold reservoir, it absorbs heat from the cold reservoir. And instead of producing work, it requires work to be done on it to move the heat from the cold to hot reservoirs.

The efficiency of a system is always output divided by input. For a heat engine, the output is work W, and the input is QH. Therefore, the efficiency is given by W/QH. Because W will always be smaller than QH, the efficiency of a heat engine will always be less than 1. Because the goal of a refrigerator is to cool off the cold reservoir, QC is the measure of its output. The input to the refrigerator is the work required to do the cooling, so the efficiency of a refrigerator is QC/W. This number is called the coefficient of performance. It's not necessarily less than 1.

So given this basic picture, can you identify which variables are given by the 18 J and 20 J figures in the problem statement?
 
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  • #11
So in this case 18J are absorbed from the cold and 20J are expelled to the hot so it needs 2J of work to run?
 
  • #12
Exactly!

For the refrigerator, you have, again, QH=QC+W, so the coefficient of performance is
[tex]\text{COP} = \frac{Q_C}{W} = \frac{Q_C}{Q_H-Q_C}[/tex]This relationship holds for any refrigerator, but for a Carnot refrigerator, you can replace the Qs with Ts to get
[tex]\text{COP} = \frac{T_C}{T_H-T_C}[/tex]Can you take it from here?
 
  • #13
Ohh so i could make them equal to each other and get 18J/2J=Tc/(296.15-Tc) to solve for Tc
 
  • #14
Right!
 
  • #15
:D thank you! I was so confused and now I get it :)
 

FAQ: Carnot Engine refrigerator temp

What is a Carnot Engine refrigerator?

A Carnot Engine refrigerator is a type of refrigeration system that uses a reversible engine and operates on the Carnot cycle, which is a theoretical model of an ideal heat engine. It is designed to efficiently transfer heat from a low-temperature region to a high-temperature region.

How does a Carnot Engine refrigerator work?

A Carnot Engine refrigerator works by first compressing a gas (usually air or helium) to increase its pressure and temperature. The compressed gas then passes through a heat exchanger, where it releases heat and cools down. Next, the cooled gas expands, causing its temperature to drop further. This cold gas is then used to cool down the desired area, and the process repeats.

What is the ideal temperature for a Carnot Engine refrigerator?

The ideal temperature for a Carnot Engine refrigerator is determined by the Carnot cycle's efficiency, which is calculated using the hot and cold temperatures of the system. The lower the cold temperature and the higher the hot temperature, the more efficient the refrigerator will be. However, in practical applications, the temperature is limited by the properties of the working fluid and the materials used in the construction of the system.

What factors affect the temperature of a Carnot Engine refrigerator?

The temperature of a Carnot Engine refrigerator is affected by several factors, including the hot and cold temperatures of the system, the efficiency of the heat exchanger, the type of working fluid used, and the design and construction of the system. Additionally, external factors such as ambient temperature and humidity can also impact the refrigerator's temperature.

How does a Carnot Engine refrigerator compare to other types of refrigerators?

Carnot Engine refrigerators are known for their high efficiency, but they are also more complex and expensive to build compared to other types of refrigerators, such as vapor-compression refrigerators. However, they have the advantage of not using any harmful refrigerants and can theoretically achieve lower temperatures than other systems.

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