Section 20.5 Compressibility
The fractional change in volume per unit change in pressure is an important characteristic of materials. This property is called compressibility, which we denote by Greek symbol \(\kappa\) (kappa). Mathematically,
\begin{equation}
\kappa = - \frac{1}{V}\,\frac{\partial V}{\partial p}.\tag{20.12}
\end{equation}
If pressure is changed while keeping the temperature constant, then we call this isothermal compressibility and denote it by \(\kappa_T\text{.}\) And if the pressure is changed by insulating the material so no heat can enter or leave the system, then we call it adiabatic compressibility and denote it by \(\kappa_\text{ad}\text{.}\)
In the next chapter we will study ideal gas law: the following relation holds for \(n\) moles of an ideal gas occupying a volume \(V\) at temperature \(T\) (Kelvin) and pressure \(p\text{:}\)
\begin{equation*}
p V = n RT
\end{equation*}
Using this equation for constant temperature, we will get
\begin{equation*}
\kappa_T = -\frac{1}{V}\frac{\partial}{\partial p}\left( \frac{nRT}{p} \right) = \frac{nRT}{p^2V} = \frac{1}{p}.
\end{equation*}
