Internal and thermal energy vs Temp?

[Austin0]

Internal and thermal energy vs Temp?

Hello I am a layman who is seriously trying to grasp the concepts and principles of physics to understand the workings of the world.
I have seen the equations for deriving Internal Energy and Thermal Energy but lack the math to apply them or be sure if I have got the concepts.
A couple of examples would be very helpful as reading hasnt brought certainty

SO if there is a volume of intermolecularly positive gas say, Oxygen ,that has been allowed to reach environmental temp [under the inversion temp] and it is then adiabatically expanded into a vacuum :
1 the temp would drop. COrrect??

2 What would be the Internal energy evaluation of the two states , compressed vs expanded? Would the internal energy level also drop or would the two states be equivalent?

3 Same question regarding the Thermal energy evaluation.

As there would be no work done and no system loss to the environment , logically I would assume the two states would be equivalent but am unsure of this.

Also regarding Ice and H2O at 0 C. Would the difference in latent heat energy show up as a lower internal/thermal energy level for the ice?

I know these questions may be elementary but they have plagued me for some time and any help would be very appreciated. Thanks

 

[FranzDiCoccio]

If the gas is ideal, there is no change in the temperature after an adiabatic free expansion. The internal energy stays the same as well (no work done, no heat exchanged...).
But I would not say that the states are equivalent, although I'm not sure what you mean by "equivalent".

I do not know what you mean by "intermolecularly positive gas" either, but sounds like you're
thinking of the "Joule free expansion experiment". Plenty of information on the web, and in textbooks of course.