When a long, straight object such as a rod or wire is stretched, most of the work is done against the tension in the rod or wire. There is also a small contribution coming from pressure forces acting on the curved surface, but these can be neglected to good approximation under many circumstances. We can therefore treat a rod of length $L$ as a closed thermodynamic system with fundamental relation
$$
\mathrm{d} U=T \mathrm{dS}+f \mathrm{~d} L
$$
The natural length $L_0$ is the length when the tension falls to zero. The strain is defined as the fractional extension, $\mathrm{d} L / L_0$ when the rod is put into tension. The stress is defined as the force per unit area, $d / / A$. The Young's modulus is defined as the ratio of stress to strain. Hence the isothermal Young's modulus is
$$
E_T=\left.\frac{L}{A} \frac{\partial f}{\partial L}\right|_T .
$$
Thermidymawic: A Cawpleve Lindergnahwer Cowrse Andrew M. Steane.
C Andrew M. Steane 2017. Published 2017 by Oxaford Lniversity Press.