Isoentropic P-T relation

We have derived the equation of state of an ideal gas under adiabatic reversible changes in week 2(‘Equation of state for adiabatic, reversible changes of ideal gases’). The equation of state in this case shows relations between temperature and pressure or pressure and volume.

We can derive this relation using a property relation. Since the adiabatic reversible change is an isoentropic change, our task is to derive an expression for pressure dependence of temperature at constant entropy. The obtained temperature-pressure relation or pressure-volume relation is the same as before for the ideal gas under adiabatic, reversible changes. The temperature change upon pressure change at constant entropy for solids is also estimated with some numerical values.