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If you blow air against your hand with your mouth open, you feel warm breath. If you do with with your lips closed except for a small opening, you feel cold breath.

One explanation from here says "With your mouth open most of the air which reaches your hand has come out of your mouth. With pursed lips lots of cold air is entrained so the air reaching your hand is cold and moving quickly."

Another explanation from Paul Hewitt video,(go to min 24:00), is that air comes out cold it because it expands coming out of small opening.

So which explanation is right?

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must be the second. –  anna v Aug 14 '12 at 3:15
    
related if not dup physics.stackexchange.com/questions/7868/… –  Yrogirg Aug 17 '12 at 4:21
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4 Answers

It's a simple enough experiment to do.

I took a kitchen thermometer and blew hard on it for as long as I could manage (about 30 seconds). With the thermometer about 15cm from my lips I got half a degree temperature rise. With the thermometer 1cm from my lips I got a 5 degree temperature rise. A quick check blowing on my wrist from 1cm confirmed that at this range the air feels warm.

So either the air current I produce is turbulent and mixes with cold air, or the air current is cooled by the surrounding air as it travels through it. Cooling due to expansion is ruled out unless there is a significant pressure gradient from 1cm to 15cm away from my mouth, and this seems unlikely.

I'm not a smoker so I can't easily examine the air flow to see if it's turbulent. I would guess that it is, but not very turbulent because the air current feels fairly localised even at a distance of 30cm. So I suspect the air current from your breath is cooled by the air around it.

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Another experiment you can do is to form a hollow tube by placing your fingers against your palm, and blow through that. This means that the air flow can't mix or be cooled by the surrounding air. If you do this it feels warm, not cold, which suggests that this explanation is correct. –  Nathaniel Aug 14 '12 at 11:26
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Do you have a thermometer?
You could test if the air is really colder or if it just feels colder

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If it feels cold sometimes and worm sometimes, then it is cold when it feels cold and warm when it feels warm. Besides this is not an answer to the question. This should have been added as a comment below the question not as an answer. –  Revo Aug 14 '12 at 3:34
    
It's hardly physics research so just writing the answer doesn't really add anything –  Martin Beckett Aug 14 '12 at 4:14
    
-1: This should have been a comment and yes, if it feels cold it is cold, and if it feels warm then it is warm. Suggesting that the air feels colder but isn't colder is like suggesting that on a boiling hot day, it's not actually any warmer than a winter day, when it obviously is. –  Olly Price Aug 14 '12 at 14:08
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Whether it feels warm or not has to do with evaporation as well as the temperature of the air flow. This answer is quite correct in suggesting that the only way to distinguish between these is with a thermometer. –  Nathaniel Aug 14 '12 at 14:53
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I think the expansion explains only part of it -- a small part I'd say.

I think the more likely explanation is that blowing with your mouth open results in an airflow that moves much slower than an airflow blown through a small opening in the lips. The faster moving air will cause a quicker rate of evaporation on your hand, which makes it feel colder.

But proper measurements are always more convincing than theories :)

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Ruling out

It's not to do with the speed that the air is coming out of your mouth. You can test this by blowing really lightly with your mouth almost closed, and then by blowing as hard as possible with your mouth wide open (so that when your mouth is closed the air flow is less fast than with the mouth open): it's still warm with your mouth wide open and cold with your mouth almost closed.

My theory

I suspect that because of the small gap when your mouth is nearly closed and the curved lips and then also different surrounding air pressures, all these would cause most of the air that's flowing from your mouth to spread out, which means that less molecules (albeit still a lot) are hitting your hand than when blowing with your mouth wide open.

Because there are less molecules hitting your hand at any one time (also less densely) you inevitably have far less energy hitting your hand as well, which in turn means less heat. Because there are more molecules hitting your hand at any one time (also more densely), there is more energy hitting your hand as well, which in turn means more heat.

Summary

So to sum up what I have just suggested, which seems to me a very liable suggestion, the difference in temperature on your hand is to do with the fact that there's a difference in the number of and density of molecules hitting your hand at any one time.

Note: I may have seemed quite ambiguous when talking about the "density" of the air hitting your hands. When I say "more dense" I mean that there's more $air/mm^2$ hitting your hand.

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