Will I heat up or cool down in empty space?

Question

Suppose I am floating in space without clothes (don't imagine it though...). Far away from the stars. Everything is as dark as the night. Including me. I can hold my breath indefinitely and my eyes are firmly closed. My body produces energy, which will make it heat up, and radiates energy, which will make it cool down. But what is the balance? Will I heat up or cool down?

Can I overcome eventual freezing (which will indeed happen according to the answer by James Hoyland when I stay at rest), by moving wildly? In rest I produce about $100(W)$, but when I run the fast I can this can be $1000(W)$. So maybe this can save my life while jumping from one spaceship to another somewhere in outer space.

Answer 1

You will reach an equilibrium temperature where the heat your body generates is equal to the heat it looses. You would radiate at a rate of $P=A \varepsilon \sigma T^4$ ( P is in Watts )where A is your surface area $\sigma$ is the Steffan-Bolztmann constant and $\varepsilon$ is your emissivity - we don't know what that is so lets take it as 1 (perfect blackbody), it would in reality be a bit less than that. Lets say surface area 1 square meter if you roll up in a ball.

So a human body at rest generates about 90W. So you would reach equilibrium when the your temperature corresponded to that power output - approximately 200 Kelvin or -75C or -100F. Unfortunately at that temperature you would already have died so you will have stopped generating that 90W and will be headed down to absolute zero!

Answer 2

The answer depends on whether or not you include pressure effects in your analysis. If you assume that your body is very strong, then it will not burst in a vacuum and James Hoyland's radiative heat transfer analysis will hold true.

If instead you assume that your body is not very strong, then you will very rapidly explode when exposed to a vacuum before significant radiative heat transfer has a chance to occur.

In the case of a Deschele Schilder "kaboom" event, the analysis would proceed as follows:

We assume for an estimate that Deschele Schilder consists entirely of water at body temperature and ambient pressure (exactly how much water is to be determined by Deschele Schilder). Assume also a spherical Deschele Schilder. We'll place a 90 watt light bulb in the center of the sphere and power it with physics magic, although it won't affect the analysis.

Then before Deschele Schilder can escape this gruesome fate, we thrust Deschele Schilder into a hard vacuum, and then very quickly consult the phase diagram for water (it would help to have the phase diagram book open to the appropriate page before the start of this experiment).

This will tell us that the spherical volume of Deschele Schilder-flavored water will experience a vapor explosion, in which the enthalpy required to effect the phase change is already stored in the water itself, so it boils into vapor all at once, everywhere within the volume at the same time.

Now we have a spherical volume of water vapor at room temperature which is allowed to freely expand into a near-vacuum, at an effective temperature of ~2.3 K, and obtain our Deschele Schilder kaboom (actually, in the airless vacuum of outer space, we wouldn't hear the kaboom but we could in principle see it).

In a free expansion, the only work performed is on the mass of the expanding material itself, which will be accelerated by the pressure inside the sphere of boiling Deschele Schilder.

Can one of the experts here pick up the analysis and estimate the departure velocity of the Deschele Schilder vapor in the vacuum? Thanks in advance ;-)