Internal energy question

[david18]

I know that molecules have kinetic and potential energy to make up internal energy. When the temperature of an object increases, the internal energy increases.

When the kinetic energy doubles, the temperature doubles as KE is directly proportional to the kelvin temperature. Does this mean the potential energy stays the same when the temperature of an object is changing? (as i know it increases when the object is changing state at constant temperature)

 

[Zeppos10]

The question posed is simple and well-formulated, but did not receive a response in 880 days, which surprises me.
What makes this question interesting is, that it raises the question whether the heat capacity (proportionality between U and T, ie dU/dT) can be spit in a kinetic energy part and a potential energy part, and whether the latter part is zero.
Specially for solids it seems evident that both heat-capacities should be positive, but it has to be worked out quantitatively.
I would say the answer to the question as posed is no.