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A friend of mine told me that if you were to stand beside plate of metal that is millions of degrees hot, inside a 100% vacuum, you would not feel its heat. Is this true? I understand the reasoning that there is no air, thus no convection, and unless you're touching it, there's no conduction either. I'm more so asking about thermal radiation emitted by it.

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I'm more so asking about thermal radiation emitted by it.

Here's a quantitative estimate.

Suppose that the hot plate remained intact long enough to do the experiment. For a rough estimate, we can treat the hot metal plate as a blackbody. According to Wien's displacement law, the electromagnetic radiation emitted by a blackbody at temprature $T$ is strongest at the wavelength $$ \lambda = \frac{b}{T} \hskip1cm b\approx 2.9\times 10^{-3} \text{ meter}\cdot\text{Kelvin}. \tag{1} $$ The total power emitted per unit area is given by the Stefan-Boltzmann law $$ \frac{P}{A}= \sigma T^4 \hskip1cm \sigma\approx 5.7\times 10^{-8} \ \frac{\text{Watts}}{\text{meter}^2\cdot\text{Kelvin}^4}. \tag{2} $$ For $T=10^6$ Kelvin, these estimates give $$ \lambda\approx 2.9\times 10^{-9}\text{ meter} $$ and $$ \frac{P}{A}\approx 5.7\times 10^{16}\ \frac{\text{Watts}}{\text{meter}^2}. $$ This wavelength is in the X-ray range, and this power level is more than a trillion times the power a person on earth would receive from the sun if there were no clouds and no air.

Would you feel it? I'm not sure. Probably only very briefly.

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    $\begingroup$ Given how slow nerve signals are compared to light, I'm pretty sure you wouldn't feel it :P $\endgroup$ – Luaan Jul 15 at 10:16
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    $\begingroup$ @Ruslan. Refrasing a comment by user Fattie: “Surely and obviously the issue that the metal would not be a metal, -or a black body, or vaporized- at that temperature, is not the point of the question. $\endgroup$ – J. Manuel Jul 15 at 11:49
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    $\begingroup$ @Ian OP specified that the test person would stand "beside the plate" and mentioned "but not touch it". So the distance is 0.1 to 1 meter. $\endgroup$ – Aaron Jul 15 at 13:52
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    $\begingroup$ @Ruslan Even if somehow the plate was only emitting 0.1% of what you'd expect from blackbody radiation, it wouldn't change much at those scales. $\endgroup$ – Eth Jul 15 at 15:03
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    $\begingroup$ Also, even if we ignore the radiation, the exploding metal plate will vaporize you before you feel anything. At a million degrees there is no such thing as a metal plate, there's only hot, dense plasma... $\endgroup$ – cmaster Jul 16 at 7:11
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The other answers provide good explanation why your friend is wrong in this case. I just want to point how you could both easily reach the same conclusion without knowing much of the physics involved:

The surface of the Sun is about 6000 degrees (Celsius and Kelvin). It is separated from you by 150 million kilometres of vacuum, yet you can clearly feel it. It follows that you could feel higher temperatures too, up until the point where you couldn't feel anything at all.

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    $\begingroup$ While true, it doesn't follow. Without broader knowledge, we might conclude that while the atmosphere around us is heated, the space beyond is not. $\endgroup$ – Strawberry Jul 15 at 16:38
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    $\begingroup$ @Strawberry I don't understand what point you're making. Are you making a distinction between locations where there is something to be heated (the atmosphere) versus where there isn't anything (outer space)? If so, then wherever you are, by definition there is something to be heated. If you are simply saying that they might be something special about the atmosphere that it absorbs heat where a human body wouldn't, there's no a priori reason to think that. $\endgroup$ – Acccumulation Jul 15 at 19:47
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    $\begingroup$ @Dronz no, if you mean the gamma rays. You don't feel the gamma rays as heat. It's thermal radiation that you can feel as heat. And the thermal radiation is a direct consequence of surface temperature. $\endgroup$ – Džuris Jul 15 at 23:35
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    $\begingroup$ @Strawberry "while the atmosphere around us is heated, the space beyond is not." That's the point, though - the atmosphere's temperature is raised to a couple hundred Kelvin hotter than it would be if it was not being heated by the Sun, and the Sun is much colder and more distant than the object hypothesised by the question. If an object with a surface temperature of 6000 kelvin separated by 150 million km of vacuum can heat something by a couple hundred kelvin, then an object at a million degrees kelvin at a distance of only a metre or so would definitely have a noticeable heating effect. $\endgroup$ – anaximander Jul 16 at 11:11
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    $\begingroup$ @JyrkiLahtonen, The radiation from the Earth's core is stopped by the layers of metal and rock above the core. The energy has to transfer via conduction, which takes a long time with something as massive as a planet. It's also why the Sun's surface is only 6kK instead of 15MK. $\endgroup$ – MichaelS Jul 17 at 7:14
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Your friend is completely wrong. Consider the following things:

  1. The temperature that you are talking about is very high, no metal would be in a solid state at the temperature you are talking about. So, before your plate reaches millions of degrees, it would have melted long before.

  2. Your understanding is correct in terms of thermal radiation. The radiation of Sun reaches Earth and there is a vacuum between. So, if you have an object as hot as you are talking about it will emit thermal radiation energy per unit time as per the Stefan-Boltzmann Equation. And remember, the rate of emitted radiation is proportional to the fourth power of temperature, so doubling the temperature would increase the rate by 16 times. You can calculate the energy reaching per unit area of your skin and find out what will happen!

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    $\begingroup$ Don't you mean the plate is going to sublimate instead of melting, since the temperature is above its boiling point? $\endgroup$ – Ferrybig Jul 16 at 8:23
  • $\begingroup$ @Ferrybig As OP has not mentioned the rate at which the temperature is raised to millions of degree, hence I haven't assumed that the temperature would rise suddenly to millions of degree. I agree that neither OP has mentioned that the temperature is rising slowly to allow the metal to melt, so I guess I get your point. It is just that I didn't feel, given the intent of the question, to be over technical about things which doesn't matter the overall message the response should convey. Sometimes, I feel being over technical when there is no need might kill the objective of conveying the insight $\endgroup$ – orion Jul 16 at 11:20
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    $\begingroup$ Funny enough, in this case I think it might sublimate; but not for the reasons ferrybig is suggesting. It also probably highly depends on the metal, I could only quickly find information on iron. If you assume an actually perfect vacuum, iron has no liquid phase at those pressures so it would sublimate, at least initially. The partial pressure of the iron vapour might be enough to get the rest to start to melt anyways once part of it evaporates. $\endgroup$ – JMac Jul 16 at 11:42
  • $\begingroup$ @JMac Well, that's a nice point, I didn't think in this direction. Thanks for posting. $\endgroup$ – orion Jul 16 at 15:01
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    $\begingroup$ @Ferrybig it's going to totally ionise instead of sublimating. $\endgroup$ – OrangeDog Jul 17 at 10:46
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A friend of mine told me that if you were to stand beside plate of metal that is millions of degrees hot, inside a 100% vacuum, you would not feel its heat. Is this true?

Not true. The "heat" concept - according to Feynman is the "jiggling of the atom". In the low temperature range these jiggling will need conduction/convection as mode of transmission of its energy - in order to transmit the "heat" via inter-atomic "jiggling".

On the other hand, these "jiggling" need not just be the atom itself, but can be the electrons that switches between energy level. These switching between electrons energy level will emits all kinds of EM waves (depending on the temperature ranges). Some of these are infrared waves. Even your toaster when hot will be emitting infrared waves, which CAN transmit through a vacuum. Just like the sun - whose energy reaches us through a high vacuum. Or your skin - and the infrared light is visible at night to night vision goggles.

Note: as someone highlighted that Blackbody radiation occurred at all temperature - True. (this is the EM waves that is emitted as mentioned above)

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    $\begingroup$ You might want to change the part where you indicate the jiggling of low temperature objects requires convection/conduction. All objects emit blackbody radiation. The intensity/energy depends on temperature - it's why predators with infrared vision can see the heat of their prey, while things heated up a few hundred degrees glow red, and why things heated up even further turn white. It may not be visible at lower temperatures, but the radiation is still happening. $\endgroup$ – Kevin Jul 15 at 21:11
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Actually, your friend is probably right but for the wrong reason. That much energy is going to fry you in very short order--and will probably kill the nerves before they can say "hot!"

Remember, energy goes at the 4th power of temperature. 100x the temperature of the sun equals 100 million times the energy. There is no question that's enough to kill you very quickly, the only uncertainty I have here is whether you will perceive anything before that happens.

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    $\begingroup$ Why the down votes? This is actually the most correct answer. Being close to something that is over a hundred times the surface temperature of the Sun is going to make you feel dead (whatever that is like). $\endgroup$ – EvilSnack Jul 16 at 0:49
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    $\begingroup$ +1'd it to zero, but it's still a bad answer because it doesn't explain why. See top voted answer for an example of the same point made well $\endgroup$ – Fred Stark Jul 16 at 1:29
  • $\begingroup$ You would not perceive anything before it happens. The energy you'd receive would be greater than that if you were to sit on a hydrogen bomb, and naturally the pressure wave from a bomb travels far slower than light. $\endgroup$ – forest Jul 17 at 6:32
  • $\begingroup$ @forest The issue is how fast nerves can sense and how fast the signals move along the nerves. The fastest signals are only about 120 m/s and it also takes the brain time to translate that impulse into a sensation. $\endgroup$ – Loren Pechtel Jul 18 at 1:06
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Thermal radiation would indeed be an issue, but there are a couple of interesting facets of this question and its answer that are obscured by the hyperbole. It's instructive to peel away the hyperbole to learn more.

First of all, "millions of degrees" is not compatible with "metal" in any familiar sense. Iron boils at 2862°C. Tungsten melts at 3422°C and boils at 5930°C[1]. At millions of degrees you would have an expanding plasma ball competing with its own thermal radiation to explode and kill you. We could postulate that something confines the plasma, and in that case the thermal radiation would cook you in short order, as explored in other answers.

However, I think your friend may have been thinking of a very real phenomenon that often gets obscured by introductory physics curricula. I don't see it mentioned here, but it has literally and metaphorically burned many people, so it's worth re-casting the question in order to highlight this phenomenon.

"If you wave your hand near a block of 660°C Aluminum, just below its melting temperature, do you feel the heat, assuming convective heat transfer is negligible?"

We are familiar with hot objects in everyday life, and we intuitively expect hot objects to radiate heat. The Stefan-Boltzmann law tells us how much power per area a blackbody radiates, and many objects in our everyday lives are decently approximated by blackbodies. Under the assumption that the Aluminum behaves like a blackbody -- which you should now be highly suspicious of -- you might intuitively expect to feel approximately the following power/area of radiated heat when you wave your hand past:

$$ \frac{P}{A}=\sigma T^4\approx (5.67 \cdot 10^{-8})(273+660)^4 \approx 4.3 W/cm^2 $$

You would feel only 3% of that. You might erroneously assume that the Aluminum has a low temperature, touch it, and burn yourself. Many have.

The reason is simply that many materials under many conditions don't behave like black bodies. Aluminum is a notorious outlier. The ratio of actual emitted thermal radiation to black body radiation is called thermal emissivity and varies quite a bit for different materials, surface finishes, and so on:

https://en.wikipedia.org/wiki/Emissivity

In the lab, this has practical consequences. You can't read the temperature of shiny metallic surfaces through a thermal camera because those surfaces will behave like mirrors, not temperature-indicating glowsticks. You can fix this problem by adding little black patches to any shiny parts you need to measure.

I startle myself at least once a year by assembling a circuit, watching it through a thermal camera for the first powerup, reaching over to turn on a power supply, and jumping back at the sudden jump in temperature due to seeing my arm's thermal reflection in the shiny components.

[1] Taken directly from the wikipedia pages for Iron and Tungsten. I believe these temperatures assume vacuum but didn't verify that. Regardless, I wouldn't expect P=1atm to fundamentally alter the discussion.

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You would feel its blackbody radiation as it is an EM wave and does not need a physical support to propagate itself. Also, "100% vaccuum" is not rigorous definition of the state of your system.

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  • $\begingroup$ The answer would be the same regardless of whether or not you're in an ultra-high vacuum or at 500 atmospheres. You'd die instantly either way. $\endgroup$ – forest Jul 17 at 6:33
  • $\begingroup$ @forest You are correct, I just pointed out a problem in the definition of the question, even though it doesn't have influence in the result. $\endgroup$ – PackSciences Jul 17 at 15:43
  • $\begingroup$ @forest Well actually at 500 atmospheres, there would be conductoconvective transfer $\endgroup$ – PackSciences Jul 17 at 15:44
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The black body answers are fine, but I would like to point out that no one has accounted for the amount of material present. If you had a metal gas with 100 atoms obeying a Maxwell-Boltzman distribution at the stated temperature, you would feel nothing.

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    $\begingroup$ 100 atoms can hardly be described as a "plate of metal" as specified in the question $\endgroup$ – John Dvorak Jul 17 at 4:45
  • $\begingroup$ Given the plate is a disc of radius X, 1 meter from the person, approximating the Sun as a disc of radius 700 Mm, 150 Mm from the person, we get 1 m=X²×15.6×10¹⁵÷441, which gives us X=170 nm radius to equal the Sun's intensity. About the size of a virus. (1 μm radius with aluminum at 3% emissivity.) I don't think that's what the OP had in mind. $\endgroup$ – MichaelS Jul 17 at 8:03

protected by ACuriousMind Jul 15 at 21:24

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