Max Heat Leak in a Refrigerator: 0.25 HP Motor & -20ºC Box

In summary, to calculate the maximum heat leak that can be tolerated by a refrigerator with a 0.25 horsepower motor, we need to first convert the horsepower to watts and calculate the coefficient of performance. Then, we can subtract the heat removed by the refrigerator from the heat produced by the motor to find the maximum heat leak. In this problem, the maximum heat leak is -62.17 Watts, meaning that the refrigerator can maintain the interior temperature at -20ºC while the motor runs continuously.
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Homework Statement



A refrigerator is operated by a 0.25 horsepower motor. If the interior of the box is to be
maintained at –20ºC against a maximum exterior temperature of 35ºC, what is the maximum
heat leak (in watts) into the box that can be tolerated if the motor runs continuously?
Assume that the coefficient of performance is 75% of the value for a reversible engine.




Homework Equations



ds=dQ/T

The Attempt at a Solution

 
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To solve this problem, we first need to calculate the heat that is being produced by the motor. We can do this by converting the horsepower to watts, which is 0.25 hp * 746 Watts/hp = 186.5 Watts. This is the amount of heat that is being produced by the motor, and it is the maximum amount of heat that can be tolerated without causing the interior of the box to warm up.

Next, we need to calculate the coefficient of performance (COP) for the refrigerator. The COP is a measure of how efficient the refrigerator is at removing heat from the interior of the box. In this problem, we are told that the COP is 75% of the value for a reversible engine, so we can use the equation COP = Qc/W to find the COP. We know that Qc = 186.5 Watts, so we can plug that into the equation and solve for W, which is the heat that is being removed from the box by the refrigerator. This gives us W = 186.5 / 0.75 = 248.67 Watts.

Finally, we can calculate the maximum heat leak that can be tolerated by subtracting the heat removed by the refrigerator from the heat produced by the motor. This gives us a maximum heat leak of 186.5 - 248.67 = -62.17 Watts. This negative value means that the refrigerator is actually removing more heat from the box than the motor is producing, which is necessary in order to maintain the interior temperature at -20ºC.

In conclusion, the maximum heat leak that can be tolerated by the refrigerator is -62.17 Watts, which means that the motor can run continuously without causing the interior of the box to warm up.
 

Related to Max Heat Leak in a Refrigerator: 0.25 HP Motor & -20ºC Box

What is a max heat leak in a refrigerator?

A max heat leak in a refrigerator refers to the maximum amount of heat that can enter the refrigerator from the external environment. It is a measure of the refrigerator's ability to maintain a constant temperature.

What does a 0.25 HP motor mean in a refrigerator?

A 0.25 HP motor in a refrigerator refers to the motor's power and indicates how much energy is required to run the refrigerator. A higher HP motor means the refrigerator has more power and can cool faster.

What is the significance of a -20ºC box in a refrigerator?

A -20ºC box in a refrigerator is a freezer compartment that is able to maintain a temperature of -20ºC. This is important for storing frozen foods and preventing them from spoiling.

How does the max heat leak affect the performance of a refrigerator?

The max heat leak directly impacts the ability of a refrigerator to maintain a consistent temperature. A higher max heat leak means the refrigerator may struggle to keep its contents cool, while a lower max heat leak indicates better insulation and efficiency.

What factors can affect the max heat leak in a refrigerator?

The main factors that can affect the max heat leak in a refrigerator include the quality of insulation, the efficiency of the motor, and the external temperature. Poor insulation or a less powerful motor can lead to a higher max heat leak, while lower external temperatures can help reduce the max heat leak.

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