On a hot day a friend suggests that you can make your kitchen cooler by leaving the refrigerator door open. Would leaving the refrigerator door open cause the air temperature in the kitchen to decrease?
No (in fact the room temperature would increase slightly)
...see note below for possible exception
A refrigerator functions as a "heat pump," transferring heat from the refrigerator's interior to its exterior compressor coils. In older models, the compressor coils were visible on the outside and could be easily checked to ensure that they heated up properly; in more recent models, the coils are enclosed but still outside the insulated refrigerator interior.
The room's overall temperature will rise because the motor needed to run the compressor pump will produce some extra heat.
If the compressor coils could be installed outside the room—for example, outside—that might be an exception.
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Leaving the refrigerator door open would not cause the air temperature in the kitchen to decrease. In fact, it would likely have the opposite effect, as the refrigerator's motor would have to work harder to maintain its internal temperature, leading to increased heat release into the kitchen. Additionally, warm air from the kitchen would enter the refrigerator, further reducing its cooling efficiency.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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