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I was reading that space is very cold and also it is a vacuum, and so my question is quite simple, if temperature is the "jiggling" of atoms and molecules and heat is distributed through jiggling particles passing the energy by hitting other atoms thus cooling or getting hotter. There is no particles in space so how can it have a temperature since it does not really pass the heat around and if so how can a object cool down in space?

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There is no particles in space so how can it have a temperature since it does not really pass the heat around and if so how can a object cool down in space?

When space is said to be cold, it does not always mean its temperature is low; it may not have temperature if the radiation present is not equilibrium radiation (which never is exactly; the radiation is influenced by the solar system objects - Sun, Earth, solar wind etc.).

What is meant is that when you put a body at common temperature into orbit or further away from the Earth into shadow (so that Sun is not directly shining on it), its temperature will quickly decrease because it will radiate and lose energy. If no external radiation is heating up the body, the rate of energy loss can be estimated with help of the Stefan-Boltzmann formula

$$ |dE/dt| = A\sigma T_{b}^4 $$

where $\sigma = 5.67E-8 W/m^2/K^4$, $T_b$ is temperature of the object in Kelvins and $A$ its surface area. For human body, this makes around 500 watts of heat loss. At this rate one would freeze very quickly.

On Earth this does not happen because the environment is full of other bodies (ground, atmosphere) that radiate back and maintain the temperature of things near common values around 300 K. Due to presence of this external radiation mitigating body's radiation losses, the above formula does not apply.

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Intergalactic space is filled with a photon gas at temperature 2.7K.

For heat transfer you don't necessarily need atoms, other particles, such as photons suffice.

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You are correct that space is not filled with jiggly stuff with energy ½ KT per degree of freedom. However, space is filled with cosmic microwave background photons. Their distribution in energy is that of a black body distribution with temperature 2.7 degK. If you put some material out in space (away from other heat sources), the material will absorb and emit photons, and eventually come to an equilibrium temperature of 2.7 degK. This makes the empty space behave just like a big hunk of 2.7 degK matter that you touch your material to. The big hunk and your material will equilibrate to the same temperature. In this sense empty space has a temperature that matter can equilibrate to.

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