One-dimensional one-atom gas
Below is a very simple model of a gas.
Here, a single atom bounces elastically in a one-dimensional cavity. It will
continue to bounce at the same speed forever if the piston does not move. If we
start the piston compressing, the atom gains speed when it bounces off the
piston. (speed after collision) = (speed before collision)+2*(piston speed).
That alone is enough to explain why a gas heats when we compress it and cools as
we allow it to expand.
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