Caitlyn Cole

2022-04-30

If I stood next to a piece of metal heated to a million degrees, but in a perfect vacuum, would I feel hot?

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.

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.

foireatoutmtw

Beginner2022-05-01Added 15 answers

"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 temperature $T$ is strongest at the wavelength

$\begin{array}{}\text{(1)}& \lambda =\frac{b}{T}\phantom{\rule{1em}{0ex}}b\approx 2.9\times {10}^{-3}\text{}\mathrm{m}\cdot \mathrm{K}.\end{array}$

The total power emitted per unit area is given by the Stefan-Boltzmann law

$\begin{array}{}\text{(2)}& \frac{P}{A}=\sigma {T}^{4}\phantom{\rule{1em}{0ex}}\sigma \approx 5.7\times {10}^{-8}\text{}\frac{\mathrm{W}}{{\mathrm{m}}^{2}\cdot {\mathrm{K}}^{4}}.\end{array}$

For $T={10}^{6}\text{}\mathrm{K}$, these estimates give

$\lambda \approx 2.9\times {10}^{-9}\text{}\mathrm{m}$

and

$\frac{P}{A}\approx 5.7\times {10}^{16}\text{}\frac{\mathrm{W}}{{\mathrm{m}}^{2}}.$

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.

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 temperature $T$ is strongest at the wavelength

$\begin{array}{}\text{(1)}& \lambda =\frac{b}{T}\phantom{\rule{1em}{0ex}}b\approx 2.9\times {10}^{-3}\text{}\mathrm{m}\cdot \mathrm{K}.\end{array}$

The total power emitted per unit area is given by the Stefan-Boltzmann law

$\begin{array}{}\text{(2)}& \frac{P}{A}=\sigma {T}^{4}\phantom{\rule{1em}{0ex}}\sigma \approx 5.7\times {10}^{-8}\text{}\frac{\mathrm{W}}{{\mathrm{m}}^{2}\cdot {\mathrm{K}}^{4}}.\end{array}$

For $T={10}^{6}\text{}\mathrm{K}$, these estimates give

$\lambda \approx 2.9\times {10}^{-9}\text{}\mathrm{m}$

and

$\frac{P}{A}\approx 5.7\times {10}^{16}\text{}\frac{\mathrm{W}}{{\mathrm{m}}^{2}}.$

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.

Kathleen Keller

Beginner2022-05-02Added 20 answers

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!

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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