What would happen to a human body in space if that body had also been blown into several pieces? Similarly, what if the body was badly burned?
I want to start by talking about the nature of space.
Fist, space is often described as cold. That's not exactly true, at least not in the way we usually think of cold. Here on earth, when we about it being cold, we're usually talking about the air being a much lower temperature than we are.
If we think about the rate of a body losing heat, a windy day at negative forty degrees is much colder than space. The wind passing over our skin will strip away our body heat very quickly and we will freeze pretty fast. That's a process called convection, the transfer of thermal energy through the flow of fluids.
In space, there is no wind. There is no air. There is no other matter to transfer your body heat into, so there is no convection. The only heat transfer process is radiation. Left in space, your body would slowly radiate away its heat.
This is where the other aspect of cold comes in. On the cold day, you may freeze quickly, but your lower limit is the temperature of the air. In our example, you would bottom out at minus forty.
This is where space is considered very cold. There is nothing around to keep your body from losing all of its heat. The lower limit is effectively absolute zero, -273°C, -459°F. That is quite chilly.
Next, while space might be considered cold, there is a very hot thing relatively nearby. You may have noticed that our planet is not at absolute zero. It can get quite warm here.
The sun is a giant ball of fusion radiating huge quantities of energy. That energy gets absorbed by matter and heats it up. So if you're in space in earth orbit and in direct sunlight, you could get heated above 120°C (250°F). More if you're closer to the sun, less if you're farther away, following an inverse-square law.
Besides being warm, the sun throws out some very high energy radiation that our atmosphere protects us from. Everything from ultraviolet through x-rays.
Also, space is effectively a vacuum. There are only a few atoms per cubic meter, more or less, depending on how close you are to a planet. A complete vacuum can sound very powerful and infinitely dangerous, but it's not really. The pressure at sea level on earth is around 100 kPa or 14 psi. The difference between the surface of the earth and space is about the same as it is between the surface and a 10 meter dive. Submarines need to worry about pressure more than spaceships.
Enough background. What does all this mean for your severed limbs in space?
First, they won't explode.
Even a whole body exposed to vacuum will keep itself together. We have an internal pressure that is very slightly greater than the atmosphere, and in space that internal pressure would cause our body would swell up like a balloon. Our skin is pretty tough and elastic, though, so it would hold us together pretty well.
A severed limb, though, is not contained. The internal pressure would push the blood and free flowing fluids out pretty quickly. It might even shoot off like a weak bottle rocket with the blood squirting one way and the exsanguinating limb in the other according to Newton's third law of motion.
The vacuum of space would have another effect on the blood, as well. It would boil.
The boiling point of a fluid is partly determined by the pressure of the environment. Like propane is liquid inside its high-pressure container and gas at atmospheric pressure. Water is liquid on earth, but would boil off into gas pretty quickly in space. That would affect the water in the rest of the limb as well. As the low pressure pulls the fluid through cell walls, the liquids would mostly vaporize away.
In not too long, maybe a matter of hours, your limb would be pretty dessicated.
Assuming your body parts were orbiting a planet, they would also be going through pretty radical freeze/thaw cycles. While they're exposed to the sun, they'd be getting cooked: heated beyond what the cells could handle, and getting a really terrible sunburn. That would accelerate the drying process and breaking down molecules on the surface.
As the limb passed into the shadow of the planet, it would get very cold. Not absolute zero kind of cold, because the planet radiates a bit of heat, but still in the negative hundred range. Rapid cooling would cause any remaining fluids to freeze, again damaging their cells and aiding in the exposure of the water to space where it would sublimate away. Also the cooling and heating would cause repeated and uneven contraction and expansion of the remains, causing structural damage and encouraging the piece to break up.
So in short, your body parts would quickly expel their free-flowing fluids, which would boil away into invisible gas and some dust, leaving a dessicated husk that would likely break apart into more dust through repeated heating and cooling cycles and being bombarded by intense radiation. I'm not sure how to determine how long it would take to completely disintegrate. Probably several years.
I hope that's gruesome enough for your needs.
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