= Thermoelastic Maxwell relation for a stretched band
{title2=$(\partial S/\partial x)_T=-(\partial f/\partial T)_x$}
Let $f\,dx$ be reversible work supplied to stretch a band. Its <Helmholtz free energy> obeys $dF=-S\,dT+f\,dx$. Equality of mixed <derivatives> gives the displayed relation. An <entropy> decrease on stretching therefore corresponds to increasing tensile <force> on heating at fixed extension. The sign follows the <force>/work convention; a restoring <force> exerted by the band has the opposite sign.
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