## Spontaneity and the performance of work

I’d wanted just to point folks to the latest essay in the CarnotCycle blog. This thermodynamics piece is a bit about how work gets done, and how it relates to two kinds of variables describing systems. The two kinds are known as intensive and extensive variables, and considering them helps guide us to a different way to regard physical problems.

Imagine a perfect gas contained by a rigid-walled cylinder equipped with a frictionless piston held in position by a removable external agency such as a magnet. There are finite differences in the pressure (P1>P2) and volume (V2>V1) of the gas in the two compartments, while the temperature can be regarded as constant.

If the constraint on the piston is removed, will the piston move? And if so, in which direction?

Common sense, otherwise known as dimensional analysis, tells us that differences in volume (dimensions L3) cannot give rise to a force. But differences in pressure (dimensions ML-1T-2) certainly can. There will be a net force of P1–P2 per unit area of piston, driving it to the right.

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The driving force

In thermodynamics, there exists a set of variables which act as “generalised forces” driving a system from one state to…

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