It is said that the body would freeze to death, if left in outer space, which is true, since the temperature is around $3$K.
But what are the flaws in this theory, in terms of thermodynamics (if we ignore the pressure and oxygen problem)?
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$\begingroup$ Quite the opposite. Your body can't dissipate its heat to empty space. Moreover, it can't perspire, so you'll overheat. $\endgroup$– lemonCommented May 29, 2016 at 16:56
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$\begingroup$ @lemon Since, outer space is vacuum, there is no medium for heat to transfer from our body to space but our body would radiate slowly and slowly drop the temperature down and die eventually? $\endgroup$– rndflasCommented May 29, 2016 at 17:00
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$\begingroup$ @lemon heat radiates from a black body even in the vacuum $\endgroup$– user116941Commented May 29, 2016 at 17:01
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1$\begingroup$ See also: physics.stackexchange.com/q/72179 $\endgroup$– GertCommented May 29, 2016 at 17:15
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1$\begingroup$ * if the perspiration evaporates due to low pressure it would take away additional heat with it*. Initially yes. But one doesn't sweat much when getting cold! $\endgroup$– GertCommented May 29, 2016 at 17:20
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1 Answer
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It is a bit of a hypothethical scenario where the body can breathe oxygen and does not rupture from the pressure difference (dissolved gases in the intestine and blood bubbling), but at the same time can evaporate and radiate freely. If we assume so, and also assume that there is no sunlight, then there are two major mechanisms for heat loss: radiative cooling and evaporation.
If the external surface area of a body is about $A=1~\mathrm{m^2}$, then the heat loss rate from radiation will be $Q=\sigma A T^4$ with $T$ in the range 273 K (freezing) to 310 K (normal body temperature). The heat loss rate is then 300 to 500 W. Subtract 100 W for the body metabolism and a body of 75 kg, assuming the specific heat of water, would decrease in temperature at a rate of about 3 K/h. So, by this mechanism alone, you would probably be dead from hypothermia in an hour or two.
Evaporative cooling is difficult to estimate. If the body surface is wet and evaporation is into a vacuum, then the evaporative heat loss rate is $$ Q = \frac{A p_v H_v}{\sqrt{2\pi M R T}}, $$ where $p_v$ is the vapor pressure of water (600 Pa at 0 °C), $H_v=41~\mathrm{kJ/mol}$ the heat of vaporization of water, $M=0.018~\mathrm{kg/mol}$ the molecular mass of water, $R=8.3~\mathrm{J/(K mol)}$ the universal gas constant and $T=273 K$ the approximate temperature. The loss rate would initially be very large at 1.5 MW, but the skin would dry out very rapidly. You would then have to wonder what happens with the nose, mouth, and lungs as the person would still be able to breathe somehow but at the same time lose a tremendous amount of heat by evaporation.
answered May 29, 2016 at 17:35
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$\begingroup$ "So, by this mechanism alone, you would probably be dead from hypothermia in an hour or two." - you're assuming that the body ceases to generate heat which is not the case... $\endgroup$– lemonCommented May 29, 2016 at 17:50
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$\begingroup$ Updated calculation. It's still "an hour or two". $\endgroup$ Commented May 29, 2016 at 18:07