Since it is in space there is no where for the heat to escape as there is no air in space to transmit that heat.
So does that mean that the ISS gets incredibly hot due to the people on there, all the electronics etc.
When it comes to cooling it, how do the pull it off as an air conditioner needs to get rid of the heat somehow.
In: 5
It indeed does need beefy cooling. You can read in detail here:
https://en.m.wikipedia.org/wiki/External_Active_Thermal_Control_System
But the gist of it is that the shedding of heat is done by the zig-zag panels sticking out the perpendicular to the flat solar panels (look up a photo of the ISS for reference). They literally radiate heat, as in emit infrared radiation proportional to their temperature. It’s quite inefficient, compared to conduction or convection, but as you correctly point out, those are unavailable in space.
In general, there are only two ways to dissipate heat in space, radiate it away like the ISS does, or dump the heat into a chunk of mass and eject/evaporate it. I just hope it’s obvious that the latter only lasts as long as there’s something to dump heat into. So once all the liquid evaporates, or a solid is ejected, that’s it, no more cooling.
Also, just because someone might be wondering, you can’t just dump infinite heat into a solid and just make it glow white, because at a certain point it’s hot enough that you’ll either damage the heat pump, or (if it can handle the temperature ) the heat will just conduct through the structure of the pump and whatever you’re mounting the heat sink to right back to the “cold” side, heating it up. At that point you’d just be generating more heat through the electricity in the pump to literally just “churn” the heat in the heat sink itself, just further increasing the temperature on the cold side. So there is a maximum temperature you can heat a heat sink to for a given temperature on the cold side. At that point you need more heat sinks.
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