What is the equation of state that relates pressure, volume, temperature, and amount of substance?

The equation that directly relates pressure, volume, temperature, and amount of substance is expressed in the form of the ideal gas law, which is represented by the equation PV = nRT. This equation clearly demonstrates how pressure (P), volume (V), the amount of substance in moles (n), the ideal gas constant (R), and temperature (T) are interconnected.

While the option provided presents a relationship (P = f(T, V, n)), it does not specify the mathematical nature of the relationship, nor does it provide a definite equation. It implies that pressure is a function of temperature, volume, and the number of moles but lacks a specific formula or expression. The real strength of the ideal gas law is its ability to quantify the relationship with a clear and meaningful equation (PV = nRT), making it the foundational equation of state in thermodynamics for ideal gases.

In contrast, options that manipulate or rearrange the ideal gas law (such as P = nRT/V or PV = T/n) would still be derived from the same fundamental equation. However, these forms do not capture the comprehensive relationship as the full equation does. The ideal gas law succinctly conveys the interconnectedness of these variables, making it the definitive