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A mechanical refrigerator or simply a refrigerator works on the reverse principle of a heat engine. Therefore, a refrigerator is a device that undergoes a heat transfer process with the help of a certain external work. In his statement on the functioning of a refrigerator, Clausius stated that a perfect refrigerator cannot function on its own; in other words, operating a system of refrigerators requires a certain amount of work to be done. The coefficient of performance gives the relationship between the heat released by the cold temperature source and the total amount of work done on the refrigerator.
Mechanical Refrigerator
A mechanical refrigerator or refrigerator is a machine that works on the reverse principle of a heat engine. The refrigerator consists mainly of the lower temperature (cold) body, which is a freezer, and the higher temperature (hot) part, which is the surrounding.
In a mechanical refrigerator, the working substance releases a certain amount of heat (Q2) from the cold reservoir at temperature (T2), a certain amount of external work W is done on the refrigerator, and heat (Q1) is released to the hot reservoir or the surroundings at temperature T1.
A refrigerator takes heat from a cold reservoir, and work is done on the refrigerator, which results in an amount of heat released into a heat reservoir. Mathematically, the expression for the heat that released in the surroundings or a heat reservoir can be given by,
Q2+ W=Q1
A refrigerator undergoes the following steps:
In the first step, a refrigerator undergoes a sudden expansion of the gas; the gas expands from a high to low pressure; this process cools down and converts it into a mixture of vapour and liquid.
In the second step, the cold fluid in the refrigerator absorbs the heat from the region; this converts it into vapour.
Step three consists of external work being done on the system; this results in the heating up of the vapour.
Finally, the heat is released by the vapour to the surroundings of the system.
The procedure comes back to the initial state and completes one cycle.
Heat Pump
A heat pump is a machine that is the same as a mechanical refrigerator.
The difference between a refrigerator and a heat pump depends on the device’s purpose.
If the purpose of using a refrigerator is to cool a portion of the system, for example, a higher surrounding temperature reservoir, the device is called a refrigerator.
On the other hand, if the device’s purpose is to pump heat into a portion of a system, then the device is called a heat pump.
Performance Coefficient of Refrigerator
Consider a refrigerator system in which a W amount of work is being done, if Q2 is the amount of heat generated by the cool temperature reservoir, and Q1 is the heat released in the surroundings,
We know, Q1 = W + Q2
The coefficient of performance (α) for a refrigerator is given by,
α = Q2/W,
Or, α = Q2/(Q2 – Q1).
Clausius’s statement for the refrigerator shows that a refrigerator cannot function without external work done.
Solved Examples
Example 1: A refrigerator is fixed to maintain an inside temperature at 10°C. If the room temperature is 34°C, calculate the coefficient of performance of the refrigerator.
Answer:
In the question, we are given the following:
The temperature inside the refrigerator is,
T1 = 10°C,
Or, 283 K
In the given situation, the room temperature is,
T2 = 34°C,
Or, 307 K
The coefficient of performance (α) is given by,
= T1/ T2 – T1
= 283/(307-283),
α = 11.79
Therefore, the coefficient of performance (α) of the given refrigerator is 11.79.
Example 2: A refrigerator is fixed to maintain an inside temperature at 8°C. If the room temperature is 24°C, calculate the coefficient of performance (α) of the refrigerator?
Solution: In the question, we are given the following:
The temperature inside the refrigerator is,
T1 = 8°C,
Or, 281 K
In the given situation, the room temperature is,
T2 = 24°C,
Or, 297 K
The coefficient of performance (α) is given by,
= T1/ T2 – T1
= 281/(297-281),
α = 17.56
Therefore, the coefficient of performance (α) of the given refrigerator is 17.56.
Example 3: A refrigerator is fixed to maintain an inside temperature at -2°C. If the room temperature is 40°C, calculate the coefficient of performance (α) of the refrigerator?
Solution: In the question, we are given the following:
The temperature inside the refrigerator is,
T1 = -2°C,
Or, 271 K
In the given situation, the room temperature is,
T2 = 40°C,
Or, 313 K
The coefficient of performance (α) is given by,
= T1/ T2 – T1
= 271/(313-271),
α = 6.45
Therefore, the coefficient of performance (α) of the given refrigerator is 6.45.
Conclusion
A refrigerator is a device that undergoes a process of heat transfer from a cold temperature source to a high-temperature source; for completing this process, a refrigerator requires a certain amount of external work done on the system.
Clausius’s statement explains that a refrigerator cannot fully function without its external work. The coefficient of performance gives a relationship between heat and work done.
