What happens to you in space? A simulation for all ages.

[Brutalicus]

So, I was reading a forum post where some misinformed fans were debating over whether a Dead Space necromorph would freeze and fall apart in space. Some reasoned that there was no heat transfer in space due to the lack of matter. Some retorted "space is cold, they would freeze." So I did the math. And since I did math I didn't need to, I have to justify it by sharing my simulation.




My assumptions
1) Radiative heat transfer only. Convection does not work in space as there is not enough medium to effectively transfer kinetic energy (heat) between particles.
2) Lumped capacitance. Temperature throughout the body is uniform. This is used when conduction (heat transfer within an object) dominates convection. Since there is no convection, I feel this is appropriate.
3) The temperature of the surrounding space is 0 K, absolute zero. This follows with the assumption of no matter and is reasonable.

Equations
1) Heat rate Q = mass*specific heat*dT/dt (rate of change of temperature)
2) Heat rate Q = surface area*surface emissivity*Stefan-Boltzmann constant (for blackbody radiation)*body temperature^4

The simulation
1) Properties of the necromorph's body. Since it was human I assume it's still kinda human.
--Mass = 125 kg or 275 lb. It's a big, badass necromorph.
--Body surface area = 2 sq. m or 21.5 sq. ft. See http://en.wikipedia.org/wiki/Body_surface_area.
--Specific heat of human flesh = 3470 Joules/kg-degree C. Note that absolute temperature in Kelvin (K) is used. See http://www.engineeringtoolbox.com/human-body-specific-heat-d_393.html.
--Emissivity of human skin = 0.97. Surface emissivity is all that is needed, so no assumptions need to be made. See http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/bodrad.html.
--Starting temperature = 296 K or 73 degrees Farenheit.

2) Selection of simulation parameters.

--Time interval = 1 hour (3600 seconds).
--Time step = 1 second. This is the window of time during which the heat rate stays constant. For a more accurate simulation, I could use 0.1 or 0.001... etc.

Code: Select all

A = 2;                  %Body surface area, m^2
m = 125;                %Body mass, kg
cp = 3470;              %Body specific heat capacity, J/kg-K

sigma = 5.67e-8;        %Stefan-Boltzmann constant, W/m^2-K^4
e = 0.97;               %Emissivity of human skin
T = 296;                %Initial body temperature, K

timeinterval = 3600;    %Time interval, seconds
timestep = 1;           %Time step, seconds
Temp = zeros(1,timeinterval/timestep);
t = zeros(1,timeinterval/timestep);
heatrate = zeros(1,timeinterval/timestep);

for time=0:timestep:timeinterval
    Temp(time+1) = T;
    t(time+1) = time;
    heatrate(time+1) = A*sigma*e*T^4;
    T=T-heatrate(time+1)*timestep/(m*cp);
end;
subplot(1,2,1)
plot(t,Temp,':')
xlim([0 timeinterval]);
ylim([0 Temp(1)*1.05]);
xlabel('Time exposed to space (s)');
ylabel('Lumped body temperature (K)');
title('How long does it take to freeze in space?  Temperature vs. time');
subplot(1,2,2)
plot(t,heatrate)
xlim([0 timeinterval]);
ylim([0 heatrate(1)*1.05]);
xlabel('Time exposed to space (s)');
ylabel('Heat removal rate (W)');
title('How long does it take to freeze in space?  Heat rate vs. time');

Just ignore all the crazy bullshit I did with the time vectors in the middle. It's good enough.

3) The results. Here they are! After a whopping HOUR in space, the necromorph's body temperature dropped by about 7 degrees. Eventually it would reach the temperature of its surroundings. Very eventually.



Conclusions and further reading
What the fuck? You don't freeze instantly in space? So Sunshine and that movie where the guy takes his mask off floating above Mars because the mission can't support x number of people are wrong? Yes, unfortunately. I was pissed to learn this, I was expecting a more dramatic curve (which would eventually cool enough to make you shatter T2-style). I was convinced I was wrong, until I did a bit of reading.

NASA ruins my perception of the world
Not convinced of my assumptions? Further reading on lumped capacitance....
.... and the Biot number, the primary criteria for making that assumption. In this case, the convection coefficient "h" is zero and the conduction coefficient "k" is nonzero. So, bam.
More on thermal radiation.
Blackbody radiation: how to determine what wavelengths this incredibly bored necromorph radiates while it waits to eventually freeze.

[rodos]

There's some info on Wikipedia about this.
http://en.wikipedia.org/wiki/Outer_space#Effect_on_human_bodies
http://en.wikipedia.org/wiki/Space_exposure

In short, exposure to vacuum is quite bad for you, but by no means instantly fatal. Rapid depressurization and suffocation are the key risks. Your skin makes a pretty good pressure suit to stop you from boiling away immediately and, as you've calculated, the radiant heat loss is quite slow.

There's been a bit of experimentation done on animals to verify this.

http://www.aerospaceweb.org/question/atmosphere/q0291.shtml

[Brutalicus]

Heh, those were some pretty good articles. I like how half of the "human exposure to space" article is a list of spacings in pop culture.

[Fivelives]

Simple answer: Temperature doesn't exist in a vacuum.
Complex answer: Temperature is a measure of the sum of the energy present in the molecules that make up an object. If no matter exists you have nothing by which to measure the temperature.

Outer space actually isn't cold at all - unless you're between an object and the nearest star. Then it's pretty cold, yeah, but it's still not absolute zero in space - close, but not quite. The average background "temperature" in the vacuum of space is 2.8 degrees kelvin or thereabouts, from energy left over from the big bang, but as you get closer to stars the radiation from those stars will cause fluctuations in your readings. Around Pluto or thereabouts, you're looking at around 35-40 degrees kelvin. Keep in mind though, that the "temperature" in space is a measure of radiation rather than what we think of as temperature in terms of hot/cold.

You'd be in more danger of being immediately microwaved from solar radiation than you would from being frozen to death. You'd freeze, eventually, but you'd be cooked first.

[Brutalicus]

You bring up a good point, that's another assumption I made without even thinking about it: no irradiation (or maybe absorptivity = 0?) of the body. I guess I've just been in denial since Heat Transfer, thinking people would magically freeze in space and shatter. No fun in the real world

edit: And yes, I think a couple kelvin is close enough, especially since convection is ignored (since, as you said, no molecules to vibrate = no temperature).

[Fivelives]

I got curious about it during my "I wanna be an astronaut!" phase while growing up.

[Brutalicus]

Man, I still wish I could walk around in space. And I'm an engineer :/

[Lightbeard]

All that over a forum post?

Kudos.

[rodos]

I believe the "temperature" of the solar wind at about 1 AU (earth orbit) from the sun is in the thousands of kelvin, but that's really not relevant for a discussion of radiant heat loss. The universe in general is pretty close to a black body of temperature 2.8K or whatever.

However, bear in mind that if you're not in the shadow of a planet, the sunlight at 1 AU distance is like a sunny summer day on Earth, but without any kind of atmospheric filtering. Astronauts have tinted visors for a reason. If you're in the sunlight, the balance of radiant heat is certainly in the "gets warmer" direction.

[Brutalicus]

True enough. And that's the "irradiation" I assumed negligible! I guess when you blow out the windows on a space station on Titan to rid the room of baddies, you probably pop out in the shade of another building or structure of some sort. Except for the part in Dead Space 2 with the solar arrays :p

[Gorlando]

I got curious about it during my "I wanna be an astronaut!" phase while growing up.

That phase ended for me when one kid asked me in kindergarten, "What happens when you run out of gas?" Of course, I later realized that space travel was a little more sophisticated than that, but I still never wanted to be an astronaut again. /shrug

[Fivelives]

Mine didn't end until I was told that you had to have uncorrected 20/20 vision (or better) to be an astronaut. This was before lasik surgery was relatively affordable.

[Skye1013]

This may or may not have anything to do with the thread... but the discussion of space "temperature" being 0K got me wondering...

Since 0K is the temperature in which cryogenics is theoretically possible, is the reason the bodies aren't preserved, because they aren't losing their heat fast enough? Obviously this is ignoring the depressurization, which I'm sure would do a number on the corpse.

[Snake-Aes]

Isn't it only 0K because there's nothing in it to have a temperature? Any body will still be bombarded with radiation, and any amount probably suffices to count as "more than 0"

[Gerunna]

Reading this lead me to a funny discovery regarding my workplace's Websense filter. I was trying to remember from freshman chemistry how depressurizing the corpse would affect the temperature.

Unfortunately the Wikipedia article on Gay-Lussac's Law is blocked for the reason of sex education. Kinda makes me wonder what kind of kinky shit my bosses are into.