# When an isolated ideal gas gets (adiabatically) compressed due to its own gravity, its gravitational potential energy increases. Does this mean its kinetic energy will reduce (due to conservation of total energy) and the gas will cool down? Does it not violate first law of thermodynamics which says an ideal gas should heat up on compression?

When an isolated ideal gas gets (adiabatically) compressed due to its own gravity, its gravitational potential energy increases. Does this mean its kinetic energy will reduce (due to conservation of total energy) and the gas will cool down? Does it not violate first law of thermodynamics which says an ideal gas should heat up on compression?
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coolng90qo
Because the particles are closer together, the gravitational potential energy is decreased, not increased. Moving things closer converts GPE to KE.
$U=-\frac{GMm}{d}$
As d decreases, U becomes more negative, so less potential energy remains.