It's a jungle out there

If you were floating around in empty space, how long would it take before most of your body freezes into ice, assuming that no biochemical processes take place in the body?

Details and Assumptions:

  • The human body can be modeled as \(70 \text{ kg}\) of water, around \(310 \text{ K}\), that is \( 37\text{ K}\) above the freezing point of water, radiating like a blackbody.

  • The surface area of the body is about \(2\ \text{m}^2\).

  • Useful constants include \(c_w = 4180\ \text{J kg/K}\) and \(\sigma = 5.67\times 10^{-8}\ \text{W/m}^2\ \text{K}^4\).


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