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By "hand fan" I'm referring to the kind of fan which is human-powered (link to Wikipedia article).

The problem is that by the second law of thermodynamics, the heat generated by operating the fan ought to outweigh the cooling that's experienced. With electric fans there's no problem since the agent doing the work isn't the person, but with hand fans, the operator is effectively heating up one part of his body to cool a different part. We expect that the heat generated is greater than the heat removed, which implies that hand fans are actually counterproductive. If we locked a person in a room with a hand fan, the room should heat up faster if he uses the fan than if he doesn't!

How is this apparent violation of the second law explained?

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  • $\begingroup$ physics.stackexchange.com/questions/16549/… $\endgroup$
    – Martin Beckett
    Feb 12, 2018 at 1:45
  • $\begingroup$ You say that this violates the 2nd law of thermodynamics as if it is actual fact. Can you or anyone else demonstrate this. In my judgment, this has nothing to do with the 2nd law. All that is required for this to work is for the heat removed from your body by the convective jrat transfer (including evaporation) must exceed the extra energy you need to matabolize to run the fan. $\endgroup$
    – Chet Miller
    Feb 12, 2018 at 3:33
  • $\begingroup$ @ChesterMiller see my comment to Ben51's answer. I'll edit the question, since the question could be clearer. $\endgroup$
    – Allure
    Feb 12, 2018 at 3:35
  • $\begingroup$ I agree with @Ben51. The extra heating of the room is obviously negligible. Otherwise we could not effectively use electric fans. $\endgroup$
    – Chet Miller
    Feb 12, 2018 at 3:41

2 Answers 2

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I think there are two misconceptions here.

First is that when a system does work on its surroundings, its internal energy is increased. This is indeed the human experience--when you exercise you get hot--but it is not a law of physics. For example, when gas in a piston is allowed to expand, lifting a weight and so doing work, it ends up cooler than when it started, not warmer. It is true that there must be some waste heat in the full cycle, which includes eating and digesting a meal, but there is no requirement for internal energy to increase during the part of the cycle when the hand fan is being operated, particularly because it is not a closed system: transfer of energy to the environment is permitted.

Second is that there is an implied assumption that the power expended to operate the fan is equal to the rate of resultant heat loss from the skin. This is a false equality. The primary mechanism of heat transfer is the evaporation of sweat, which is enhanced by the moving air. There is no reason this latent heat flux cannot be substantially larger than the rate at which work is done on the fan. In fact, even if there were no sweat and heat transfer occurred only by conduction, it could still be larger than the fan work without violating any laws.

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  • $\begingroup$ Wait, if we sit a person + a hand fan in a closed room, and he decides to use the fan, the room will get hotter faster than if he doesn't use the fan, correct? If this is correct, then we end up with more heat by using the fan than not, which should apply regardless of how human bodies lose heat (sweat) + is an apparent contradiction (?) $\endgroup$
    – Allure
    Feb 12, 2018 at 2:19
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    $\begingroup$ Yes, the closed (insulated) room gets hotter if you turn chemical energy into thermal energy by waving a fan. But 1) the room air is generally cooler than the skin, so the person can cool without the total energy in the room decreasing, and 2) in general rooms are not perfectly insulated. The fan is a tool which helps you transfer heat from your body to the outside world. $\endgroup$
    – Ben51
    Feb 12, 2018 at 2:25
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"the heat generated by operating the fan ought to outweigh the cooling that's experienced. " This is not obvious. A fan drives cooler air to replace the air warmed by human face.

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  • $\begingroup$ Who says? The reason it is not obvious is because it is not correct. $\endgroup$
    – Chet Miller
    Feb 12, 2018 at 3:37
  • $\begingroup$ @ChesterMiller : So I guess I am more comfortable with understatements than you are:-) $\endgroup$
    – akhmeteli
    Feb 12, 2018 at 3:54
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    $\begingroup$ Remember, car engines cool themselves with fans too. $\endgroup$
    – Tom B.
    Feb 12, 2018 at 4:50

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