You heat apiece of iron from 200 to 400 k. what
happens to the atoms' energyof random motion?

when a piece of iron is heated from 200 kelvin to 200 kelvin, the kinetic energy of molecule increases which causes the random motion of molecules in random direction faster than before.

Explanation:

when a piece of iron is heated from 200 kelvin to 200 kelvin, the kinetic energy of molecule increases which causes the random motion of molecules in random direction faster than before.  

we know that Temperature is inversely proportional to inter molecular attraction, thus whenever temperature increases the forces that bind the molecules together are dissipating hence particle moves in random motion.