Irodov Problem 2.24

Isothermal compressibility measures how much a fluid's volume shrinks under pressure at constant temperature—it's the inverse of how "stiff" the gas is. For a Van der Waals gas, you need to find $\frac{\partial P}{\partial V}$ from the Van der Waals equation, then use the definition $\kappa = -\frac{1}{V}\frac{\partial P}{\partial V}|_T$ to get compressibility as a function of $V$ and $T$. The key is recognizing that the Van der Waals corrections (molecular volume and intermolecular forces) change how pressure responds to volume changes compared to an ideal gas.

Isothermal compressibility measures how much a fluid's volume shrinks under pressure at constant temperature—it's the inverse of how "stiff" the gas is. For a Van der Waals gas, you need to find $\frac{\partial P}{\partial V}$ from the Van der Waals equation, then use the definition $\kappa = -\frac{1}{V}\frac{\partial P}{\partial V}|_T$ to get compressibility as a function of $V$ and $T$. The key is recognizing that the Van der Waals corrections (molecular volume and intermolecular forces) change how pressure responds to volume changes compared to an ideal gas.