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What if instead you consider "thermal energy" to be connected somehow to
temperature?
That actually seems to me to be the more direct connection;
'heat' only gets into the question by way of the colloquial usage where
heat=temperature.
Now does it seem strange that the expanding gas looses "thermal energy"
even with no heat tansfer?
Note: Not that I prefer "thermal energy" over "internal energy"
necessarily, but I have to admit that it seems more descriptive.