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I have this problem from University Physics with Modern Physics (13th Edition):

The inside of an oven is at a temperature of 200°C (392°F). You can put your hand in the oven without injury as long as you don't touch anything. But since the air inside the oven is also at 200°C, why isn't your hand burned just the same?

What I understood from this problem is that my hand won't be as hot as the air temperature, but then my first conjecture was: It’s the nature of the air (i.e., a gas) that its molecules are more disperse than those of a solid.

Is my reasoning right? Or what thermodynamics concepts do I need to understand better to tackle this problem?

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    $\begingroup$ Fun fact: This question's similar to why static discharges don't usually injury people despite their high voltage. In both cases, there's high potential (high temperature or voltage), but that potential rapidly falls once it comes into contact with the human body. The initially high potential ensures that part of the energy is forced on the human body, but it falls off too quickly to transfer a destructive amount of energy. $\endgroup$ – Nat Jan 30 '17 at 7:20
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    $\begingroup$ I think the issue is well demonstrated by mentioning that a domestic sauna can easily be set at 90degC and people sit inside for 15 minutes at a time. Temperatures could reach 110degC and times of 10 minutes in crazy competitions with significant additional humidity. Eventually radiant heat will cook your hand unless only the air is hot and then convection will cook it if the air temperature is actively maintained. - en.wikipedia.org/wiki/Sauna#History - en.wikipedia.org/wiki/World_Sauna_Championships $\endgroup$ – KalleMP Jan 30 '17 at 9:17
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    $\begingroup$ If you were to construct a custom oven door with a hand-sized portal in it, pre-heated the oven to 200 degrees, opened the portal, and then quickly stuck your hand through the portal, you'd burn your hand much quicker. (NOTE: actually attempting this would be ill-advised) $\endgroup$ – Dr. Funk Jan 30 '17 at 17:21
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    $\begingroup$ Likewise, if you stuck your hand in a convection oven operating at 200 degrees, you would very quickly get burned. $\endgroup$ – Dr. Funk Jan 30 '17 at 17:32
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    $\begingroup$ Your question is "if I put my hand in an oven for not enough time to burn it, why is it not burned?" The question kind of answers itself when you phrase it that way, no? $\endgroup$ – Eric Lippert Jan 31 '17 at 17:41

10 Answers 10

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There are two points relevant for the discussion: air itself carries a very small amount of thermal energy and it is a very poor thermal conductor.

For the first point, I think it is interesting to consider the product $\text{density} \times \text{specific heat}$, that is the amount of energy per unit volume that can be transferred for every $\text{K}$ of temperature difference. As of order of magnitudes, the specific heat is roughly comparable, but the density of air is $10^3$ times smaller than the density of a common metal; this means that for a given volume there are much less "molecules" of air that can store thermal energy than in a solid metal, and hence air has much less thermal energy and it is not enough to cause you a dangerous rise of the temperature.

The rate at which energy is transferred to your hand, that is the flow of heat from the other objects (air included) to your hand. In the same amount of time and exposed surface, touching air or a solid object causes you get a very different amount of energy transferred to you. The relevant quantity to consider is thermal conductivity, that is the energy transferred per unit time, surface and temperature difference. I added this to give more visibility to his comment; my original answer follows.

Air is a very poor conductor of heat, the reason being the fact that the molecules are less concentrated and less interacting with each other, as you conjectured (this is not very precise, but in general situations this way of thinking works). On the opposite, solids are in general better conductors: this is the reason why you should not touch anything inside the oven. Considering order of magnitudes, according to Wikipedia, air has a thermal conductivity $ \lesssim 10^{-1} \ \text{W/(m K)} $, whereas for metals is higher at least of two orders of magnitude.

I really thank Zephyr and Chemical Engineer for the insight that they brought to my original answer, that was much poorer but got an unexpected fame.

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    $\begingroup$ It's absolutely correct that it's about the rate of heat transfer due to thermal conductivity. It is NOT simply that air is a gas not a solid. There are solid areogels that you can pick up and handle at 200 degrees. Touching wood might hurt soon but even a brief touch from metal will leave you with a burn. It's not the so much the phase state of the matter. It's the material. $\endgroup$ – candied_orange Jan 29 '17 at 21:47
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    $\begingroup$ @ChemicalEngineer Another missing point is that, as soon as you open the oven door, a large fraction of the hot air in the oven will whoosh straight out and be replaced by denser, room-temperature air. $\endgroup$ – David Richerby Jan 31 '17 at 10:31
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    $\begingroup$ @DavidRicherby: Extrapolating from stays in a 110 degree sauna repeatedly, I don't think that the air getting out is that much of an issue... $\endgroup$ – DevSolar Feb 2 '17 at 12:21
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    $\begingroup$ @DavidRicherby: I wanted to point out that, while being a point to consider, it is unlikely to be a major contribution to the effect, citing collaborating evidence. Weak, I know. $\endgroup$ – DevSolar Feb 2 '17 at 12:35
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    $\begingroup$ "Even a brief touch from metal will leave you with a burn." Not necessarily. The amount of matter is crucial. Consider a layer of Al foil covering your roast. Even if the oven has been at say 200C for an hour, you can pull the foil off and even crumple it up to toss it away, and all you will feel (well, all I feel) is a fleeting sensation of heat. Yes, it's metal, but it's not very much metal, so the energy stored in it is low. Another factor: your flesh is mostly water and water takes more energy per degree to raise its temperature than just about anything. $\endgroup$ – Jamie Hanrahan Feb 2 '17 at 18:33
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my first conjecture was: It’s the nature of the air (i.e., a gas) that its molecules are more disperse than those of a solid.

Yes, but you can go a few steps further. The sparseness of molecules has two crucial consequences:

  • A low heat capacity – since there are few molecules to store kinetic energy.

    Air has a heat capacity of about $1\,\frac{\text{J}}{\text{gK}}$. Assuming that your oven is a $40\,\text{cm}$ cube, your hand would have to absorb a thermal energy of

    $$(0.4\,\text{m})^3 · 1\,\frac{\text{J}}{\text{gK}} · (200°\text{C}-37°\text{C}) · 1.2\frac{\text{kg}}{\text{m}^3} = 12.5\,\text{kJ}$$

    to cool this air to your body temperature ($37°\text{C}$). Solids have a much higher heat capacity per volume. For example, a piece of iron would have to weigh $186\,\text{g}$ to store the same energy (by heating body temperature to $200°\text{C}$); that’s about four spoons. Now touching a spoon at that temperature will burn you, but the heat is concentrated to a much smaller volume.

  • A low thermal conductivity – since there is fewer interaction between molecules. However, in contrast to solids, gases allow for convection, which somewhat alleviates this effect.

    The pure thermal conductivity (i.e., without convection) of air is about $0.26\frac{\text{W}}{\text{mK}}$, while that of iron is for example around $80\frac{\text{W}}{\text{mK}}$. In general, metals have a high heat conductivity, even in comparison to other solids.

    On the other hand, convection, which is the major contributor to heat transfer in air, is more difficult to quantify.

To burn your hand, you need to transfer a high amount of heat to it in a short time. For this, you need both the heat and means to transfer it. A piece of metal is much better suited to this purpose than a volume of air due to the above reasons.

The following everyday experiences are also due to these or similar effects:

  • If you run around naked at room temperature, wearing shoes or having a carpet may crucially affect your comfort – because the floor is more effective in draining heat from your body than the air around you.

  • At room temperature (and below), metal feels cold – because it drains heat from your body faster than normal solids or air.

  • In summer, it may be a bad idea to touch a piece of metal that has been exposed to the sun – because it transfers heat to your body faster than the air around you and most other objects.

  • It’s no problem to touch baking paper from your oven – because it has little mass/volume/molecules and thus cannot store enough heat to burn your hand.

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  • $\begingroup$ Also, I'd guess that by far the dominant heat transfer mechanism when sticking a hand in the oven would not be conduction through the hot air, but rather the heat radiation from the oven walls, even in a home oven. A few watts of conductive heat transfer can't really compare to hundreds of watts of radiation (assuming the oven is closed with your hand inside, of course - there will likely be significant loss of efficiency if you keep the door open). $\endgroup$ – Luaan Jan 30 '17 at 14:50
  • $\begingroup$ @Luaan: I can’t say right now how heat transfer through radiation compares to heat transfer through air (convective and conductive). However, heat transfer through radiation is present whether you touch something or not, so is not relevant for the comparison. Also, it evidently does not suffice to burn your hand. $\endgroup$ – Wrzlprmft Jan 30 '17 at 14:57
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    $\begingroup$ Great answer in general but the one about the metal in the sun is a poor example. Metal tends to absorb/retain more heat from the rays of the sun directly especially if it's a dark color like a bronze statue. I think you would find is actually at a higher temperature than something like a plant or a beach ball if you tested it. $\endgroup$ – JimmyJames Jan 31 '17 at 17:26
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    $\begingroup$ @JimmyJames: Absorption plays into this, sure, but metal is even bad in comparison to other absorptive materials. And exposing to the sun is necessary to get sufficiently high temperatures to notice something in the first place. $\endgroup$ – Wrzlprmft Feb 1 '17 at 8:15
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    $\begingroup$ My point is that the temperature of items in the sun is different which confuses the explanation because it's about how two substances of the same temperature can feel hotter or colder based on conductivity and convection. One of the best examples that many people should be familiar with is how on a cold morning a toilet seat feels much colder than the hand towels. $\endgroup$ – JimmyJames Feb 1 '17 at 16:18
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Your hand is not burned because its temperature is not at 200degC. If your hand stays there for a long time, it will be burned (i.e. the temperature will be high). So it takes time to heat up your hand. There are several factors you can consider.

The dominant heat transfer is pretty much free convective heat transfer which is low in heat transfer rate. It relates to thermal conductivity but is not really.

Your hand is not dry but is has water. When it is heated up, the water evaporates. Evaporation takes heat and protects your hand. If your hand is wet, that is even more safe.

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The effect is the same as staying in a dry sauna in which the air temperature is a 100 degrees celsius. As long as you stay put, you can stay in the sauna for a considerable time, because the air is a bad conductor of heat (putting your body onto a metal at the same temperature as in the sauna will almost immediately cause burning wounds). But as soon as you are going to move, you can't stay too long in the sauna because of the transport of heat by convection, which heats you up very quickly. Try moving your hands in the oven, and feel how fast they get hot.

You can see the same effect in very cold air surrounding you. If you experience no wind you can stay a fairly long time in the cold air (even in air of about minus 100 degrees), again due to the low heat conductance from your skin to the surrounding air. But when you walk through the cold air during a storm the windchill is gonna be such that you can't stay in the cold air too long, because of the same transport of heat by convection, which cools your skin much faster than by heat conduction alone.

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After the oven has run for a few minutes, the oven and the air inside it reach the target temperature (let's assume 200°C, but can vary depending on settings). However, in order to insert your hand in the oven, you will have to open the door. When you open the door, the hot air exits quickly. Then, the air inside the oven cannot get near 200°C because air is a poor thermal conductor and takes time to heat up. Since you have the door open, the inside of the oven will be replenished with cold air as the hot air raises and leaves the oven. Of course, all of this assumes that you don't close the oven's door with your hand inside.

The air that immediately exits the oven as you open it indeed has 200°C. But cannot be in contact with your hand for more than a few moments since it raises quickly. This is way to short for the air to be able to transfer enough heat to your hand to harm you usually, but don't try this at home.

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    $\begingroup$ This is all totally correct but (in contrast to my other comment above) you're forgetting the overwhelming difference in thermal momentum of air compared to metals and most solids. $\endgroup$ – Fattie Jan 30 '17 at 23:42
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    $\begingroup$ This implies that you would burn your hand (quickly) if you were to stick it inside in a way that did not let the hot air leave. Is this true? $\endgroup$ – Dennis Jaheruddin Feb 1 '17 at 16:35
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    $\begingroup$ @DennisJaheruddin If the hot air wouldn't leave, you will get burns. It would basically be cooked, as you cook meat. The problem (which has been pointed multiple times) is that the thermal transfer between the air and the hand is not the best, so for a few seconds you will probably be fine, then you will get burns of various degrees and, after a few tens of minutes/hours, you will have a perfectly cooked hand. $\endgroup$ – Paul92 Feb 1 '17 at 16:42
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Air is not a very good conductor. Just look at your cake as an example. If air was a good conductor of heat you'll be eating black cake!

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    $\begingroup$ If I baked a cake at 200C, it probably would be black by the time the middle had cooked. :-P $\endgroup$ – David Richerby Jan 31 '17 at 10:34
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Note that this effect is not exclusive to air, but can be observed with any materials which have low thermal conductivity. For instance, here's a guy holding a glowing-yellow (around 900°C) chunk of aerogel with his bare hand, just out of the furnace:

enter image description here

(taken from this youtube video).

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Besides all the good answers given, one thing not mentioned is that the hand is being actively cooled by, e.g., the circulation of blood (and as overclockers know, liquid-cooling is in many respects superior). As such, the hand could likely remain in the oven indefinitely, as it has the remaining mass of the human body to dump the heat into.

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    $\begingroup$ @Jmac That would depend on the heating element. If there's a red hot resistive heater right above the hand (that's usually the case) its radiation will burn. Another common method is a fan blowing hot air. That might be fine. $\endgroup$ – LLlAMnYP Jan 30 '17 at 12:30
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    $\begingroup$ A sauna is different than forced convection. It's free convection that isn't supposed to cook things. An oven is forced convection for the purpose of cooking. Extended exposure times are a bad idea. $\endgroup$ – JMac Jan 30 '17 at 13:11
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    $\begingroup$ Blood doesn't carry much heat away. It is in fact the cool, room temperature air flowing through the oven that keeps your hand relatively cool. $\endgroup$ – Dr. Funk Jan 30 '17 at 17:30
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    $\begingroup$ @Dr.Funk Ultimately, though, I believe this is an important factor. The skin will begin heating the living papillary dermis, which swiftly dies if not actively cooled; most living mammalian tissues swiftly die at anything much higher than 40C. The heat would otherwise reach the PD in a few seconds. And you can do a great deal better than even 40C even if you sit in a sauna at 100C for the best part of an hour as long as you've plenty to drink. You'd certainly know about it (you'd feel thoroughly dreadful) if significant chunks of your body got even much above 38C in the sauna. $\endgroup$ – WetSavannaAnimal Jan 31 '17 at 0:08
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    $\begingroup$ @descheleschilder Of course it's greater. The question is, as commenters brought up, exactly how much greater, given the possible range of conditions in an oven. $\endgroup$ – LLlAMnYP Feb 2 '17 at 11:31
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Just to go one step further: think about the same experiment, but now the oven is filled with water vapor at 200C rather than air.

The heat capacity and thermal conductivity of water vapor is about as bad as that of air. But you would still be severely burnt !

The difference is that water vapor would condensate on your hand, releasing its latent heat.

So hot air is not burning you because its heat capacity is small (it takes little heat to change its temperature a lot), because its thermal conductivity is small (air does not conduct well heat from the walls of the oven to your hand) and because it is not changing state at the contact of your hand.

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  • $\begingroup$ @DSuchet-Do you mean with "water vapour" steam? $\endgroup$ – descheleschilder Feb 2 '17 at 10:37
  • $\begingroup$ Yes. But remember that steam in not the cloudy stream that comes out of the teapot - this is droplets of liquid water. Steam is invisible just like air. $\endgroup$ – DSuchet Feb 2 '17 at 11:11
  • $\begingroup$ So it's air with a very high humidity? $\endgroup$ – descheleschilder Feb 2 '17 at 11:16
  • $\begingroup$ "Air" is a mixture of mostly N2 and O2, with a little bit of Ar and H2O. Humidity is the ratio between the water vapor partial pressure, and its saturation pressure at the same temperature. When I say "filled with steam", I mean steam at a vapor pressure of 1 Atm - ie no N2 or O2 left. $\endgroup$ – DSuchet Feb 3 '17 at 0:48
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Air is not heat conductive enough to transfer enough heat energy in a short enough time for it to register as particularly painful. Try keeping your arm in there for a little longer though and it might start to become a bit too crispy for your taste.

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protected by Qmechanic Jan 29 '17 at 6:17

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