# What are the problems in the idea that a person would freeze to death in outer space?

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)?

• Quite the opposite. Your body can't dissipate its heat to empty space. Moreover, it can't perspire, so you'll overheat. – lemon May 29 '16 at 16:56
• @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? – rndflas May 29 '16 at 17:00
• @lemon heat radiates from a black body even in the vacuum – user116941 May 29 '16 at 17:01
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.