# Freezing in Space I - Blackest Night

In the last post I made, I discussed the fact that humans radiate
energy.
In that post I calculated that we actually radiate quite a lot of power.
This immediately raises a few questions, the most obvious one being: How
long would it take you to freeze in space? This question is
multifaceted, and I'm going to split it between two parts. This first
part, 'Blackest Night' is how quickly we'd freeze if we were completely
lost in space, nothing anywhere near. The second part, 'Turn On The
Sun!' will address what would happen in near earth orbit. We need to
clarify what we mean when we say freezing in space. The fatal
temperature change for a human is (according to the all knowing
internet), roughly a drop of 7C. If you remember my previous post, we
calculated that we would radiate about 860 W. Now, we have to ask how
much energy it takes to change our temperature by 7 C. Well, as I've
discussed a
few
times,
the energy it takes to change the temperature is given by $$Q=mc\Delta
T$$ The mass of a human is \~75 kg. We're mostly water, so let's just
assume that we are all water. This gives us a specific heat of 4.2
kJ/kg*K. The energy needed for our 7 C temperature change is then
$$Q=(75kg)(4.2kJ/kg*K)(7K)=2.2 MJ$$ By the time we have dropped to 30
C, we are only radiating a power of $$P=eA\sigma
T^4\=(.97)(1.7m^2)(5.67\cdot10^{-8}W/m^2K^4)(303K)^4=790W$$ Let
us assume that the average power radiated is the geometric average of
these two powers, $$P_{avg}=\sqrt{(860W)(790W)}\approx825W$$ This
gives us a time to freeze of $$t=\frac{2.2MJ}{825W}\approx2700s$$ This
is \~45 minutes. So you've got 45 minutes until a deadly freeze in deep
space. Seems a rather long time, does it not? I'm fairly certain that
you'd freeze much faster in antarctica than deep space. Why? Because in
Antarctica you have more cooling mechanisms that just radiation, you
have conduction in the air around you and convection of that warmer air
away from your skin. If you're adrift in space, for all that it is
rather cold, the good news is that you'll asphyxiate before you freeze!
All of this was done assuming that there's no energy gain from anywhere.
That is, that we're stuck somewhere in the deepest space, the blackest
night. Tomorrow we'll consider what would happen if you were in near
earth orbit, with all of these lovely energy sources around,
particularly the sun.

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