The thermoelastic effect is the temperature change that results from stretching an elastic material or fiber. The work done on the material is given by W? = force × rate of change of distance = A⋅ L⋅σ ⋅
dε/dt
where σ = stress = force/cross - sectional area =
force/A
and
dε/dt = rate of strain = (1/L)(dL/dt)

In the situation being considered here, the thermodynamic properties such as the heat capacity depend on the stress (just as for a gas the heat capacity depends on the pressure).
a. Develop the energy and entropy balances for this one dimensional material, assuming that there is no additional work term other than the stretching work, and that the volume of the material does not change on stretching (that is, the length change is compensated for by a change in cross sectional area.