The ideal gas law, PV=nRT, is limited to ideal gases, and for real gases, the Van der Waals equation is commonly used, represented as (P+a*(n/V)^2)(V-nb)=nRT. This equation adjusts for the volume occupied by gas molecules and accounts for intermolecular interactions, with constants a and b specific to each gas. While Van der Waals is often sufficient for many applications, more complex equations like Beattie-Bridgeman and Benedict-Webb-Rubin provide greater precision but are harder to apply. In general, the ideal gas law remains effective at high temperatures and low pressures, and computational methods are increasingly used to derive equations of state for real fluids. Understanding these equations is essential for modeling various systems, including biological processes.