Thermodynamics: Refrigerator

In summary, in an isolated room with a mass of 500 kg of air and a specific heat capacity of 714 J/kg, a refrigerator consumes 50W of electric power. Assuming stationary work, the rate of heat transfer from the refrigerator is also 50W and after 1 hour, the temperature in the room will increase by approximately 0.5 K. This calculation is based on the assumption that the temperature inside the refrigerator remains constant and that all the power is used for heat transfer. Using Carnot's cycle is not applicable in this situation, as the stationary mode of work is assumed and no other necessary data is provided.
  • #1
irycio
97
1

Homework Statement


In an isolated room there is a refrigerator. The refrigerator consumes electric power P=50W.
Mass of the air in a room m=500 kg, and it's specific heat capacity c=714 J/kg. Calculate the stream of heat (dQ/dT) from the refrigerator assuming it's stationary way of work and how will the temperature in the room increase after t'=1h.


Homework Equations


[tex]P=\frac{W}{t} [/tex]
[tex]Q=c m \Delta T [/tex]
1st law of thermodynamics

The Attempt at a Solution



Now, the exercise seems to be extremely simple or I completely misunderstand it.
Due to the stationary way of work, we expect the temperature inside the refrigerator to remain constant. Thus, the heat entering it should be equal one leaving it, and all the power should be used for this heat transfer. Hence:
W=Q (since the total change of energy should be 0)
[tex] \frac{dW}{dt}=\frac{dQ}{dt}[/tex]
[tex]\frac{dQ}{dt}=P=50W=\frac{Q}{t} [/tex]

And regarding the increase in the temperature:

[tex]Q=cm \Delta T [/tex]
[tex]\Delta T=\frac{Q}{cm}=\frac{P*t'}{cm}=\frac{50*3600}{500*714} \approx 0.5 K [/tex]

Which seems to be quite a reasonable result.

Anyway, please correct me if I'm wrong. I mean, I was thinking of using Carnot's cycle for this exercise, but that doesn't seem to apply to this situation, as we assume the stationary mode of work. Furthermore we are not wprovided with ANY data necessary, like the temperature or thermoinsulation of the refrigerator or whatever.
 
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  • #2


Your analysis is correct. The rate at which heat is removed from the fridge is the same as the rate at which heat enters the fridge (the question omits the complexities of an actual fridge which uses a thermostat).

So the heat delivered to the room is the Qh of the refrigerator less the Qc that leaks back and is subsequently removed.

From the first law: Qh = Qc + W

Net heat contributed to the room, therefore, is Qh-Qc = W = 50 W.

AM
 

1. How does a refrigerator work?

A refrigerator works by using the principles of thermodynamics to transfer heat from the inside of the refrigerator to the outside, resulting in a cooler interior temperature. This is achieved through a series of components such as a compressor, condenser, evaporator, and expansion valve, which work together to create a continuous cycle of refrigerant fluid that absorbs and releases heat.

2. Why is it important to maintain proper temperature settings in a refrigerator?

Maintaining proper temperature settings in a refrigerator is important for several reasons. Firstly, it ensures that food is kept at a safe temperature to prevent bacterial growth and food spoilage. Secondly, it helps to keep food fresh for longer periods of time. Additionally, maintaining proper temperature settings can also save energy and reduce electricity costs.

3. What is the ideal temperature for a refrigerator?

The ideal temperature for a refrigerator is between 35-38°F (1.7-3.3°C). This temperature range is low enough to prevent bacterial growth, but not so low that food freezes. It is important to regularly check and adjust the temperature settings to ensure that the refrigerator is maintaining this ideal range.

4. How does the thermodynamics of a refrigerator differ from that of an air conditioner?

The thermodynamics of a refrigerator and an air conditioner are similar in that they both use the principles of heat transfer to cool a space. However, the main difference is that a refrigerator absorbs heat from the interior and releases it to the exterior, while an air conditioner absorbs heat from the exterior and releases it to the interior. Additionally, the components and functions of each system may vary slightly.

5. Can a refrigerator run indefinitely?

No, a refrigerator cannot run indefinitely. The components of a refrigerator, such as the compressor and condenser, can wear out over time and may need to be replaced. Additionally, if the refrigerator is not properly maintained or the temperature settings are not correct, it may not function properly and could potentially stop working altogether.

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