Do the molecules of a gas move randomly when they aren't colliding?
no. if there are no collisions each particle will act like a billiard ball, with angles of incidence equal to angles of reflection.
does the temperature of a body depend on the internal energy of it?
yes, since U=TdS-PdV, which means the internal energy is equal to temperature times a small
change in entropy minus pressure times a small change in volume.
If you increase the potential energy are you increasing the temp?
i don't think so. if we increased the mass of Earth i don't think temps would change. if we compressed a spring, the mass on the end would not get hotter.
imagine you have a partitioned system at thermal equalibrium. is there any potential we can add to one side that would cause heat transfer as a direct cause and not due to the effects of masses or charges moving?
i would imagine decreasing the PE of one side would influence particles from the other side to find a lower energy until at equlibrium, meaning decreasing the potential would increase the probability of positive influx. this arguabley means that the high PE side is hotter than the low PE side, but i think this is a mixed up analogy (based on "hot stuff flows into cold stuff").
even the definition of temperature is a bit confusing... something like "the thing that remains constant as energy changes with entropy" or T=dE/dS. I think we have to consider the center of mass frame to determine temperature, otherwise thermal motion gets confused with
the motion
if we consider 8 inert atoms in a zero kelvin solid lattice and increase the mass of the planet they are on, will this increase the temperature? there may be an increase in motion to find the new lowest energy states and the system will oscilate, becoming dampened with time, until it is at rest again... unless it oscilates continually, thereby increasing its temp for a long time.
but i still don't think potential energy increases temp... just a gut feeling though