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In a first attempt (please note that it is only an approximation) you can consider the law of ideal gases which says

pV = nRT

where p is the pressure, V the volume, nthe number of moles, R is a constant and T the temperature.

So you can see that

T = p · V/(nR)

If V/(nR) is a constant, you can see immediately that the higher the pressure the higher the temperature (they are proportional magnitudes).

If you want a deeper understand, you have to know that the kinetic theory of pressure establishes a direct relationship between pressure and speed (in an informal way, pressure is a consequence of collisions between gas particles and the walls in which they are confined). So the higher the speed the higher the pressure.

In addition to this, the speed is related to the temperature across the virial theorem, which establishes that T is proportional to the speed squared.

So, as we showed in the firsts lines, an increment in the pressure cause an increment in the speed and, consequently, an increment in the temperature.

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Q: Why temperature increases when a gas is compressed?
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