Work done by a gas during a quasi-static volume change

A volume change, i.e. the contraction or expansion of a container, is a mechanical change — and therefore any energy transferred due to this process will be work. The amount of work due to an infinitesimal quasistatic volume change is

where for an expansion and for a compression.

Derivation

Consider a container of an ideal gas expanding in one direction. The gas therefore exerts a force due to pressure, resulting in a displacement in that one direction. The total volume change will be , where is the normal area vector:

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