# Is kinetic energy proportional to temperature for non-gases?

If the molecules in a sample of ice at $$\pu{-15 °C}$$ and $$\pu{1 bar}$$ all have their kinetic energy doubled, then what is the final phase?

The answer is gas, but I am not sure how to get this answer.

I was wondering if the equation $$\displaystyle k = \frac{3}{2}RT$$ still holds in this case, even though the molecules are not a gas. It seems as though it does (it gives the right answer because $$2 \times \pu{258.25 K} = \pu{516.3 K},$$ which is a gas), but I am not too sure why.

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• Note that the mean kinetic energy is proportional to absolute temperature for monoatomic gases only. For other gases only in temperature region where vibration is frozen at the base level. – Poutnik Dec 30 '19 at 10:55