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Simple compressible systems and the state postulate

For many engineering fluids, the dominant mechanical work mode is compression or expansion against pressure. Such a model is called a simple compressible system.

For a simple compressible pure substance in equilibrium, two independent intensive properties are sufficient to fix the thermodynamic state. This is a useful form of the state postulate.

For example, specifying pressure $p$ and temperature $T$ often determines the corresponding specific volume $v$ through the substance's property relations.

The word independent matters. Inside a two-phase liquid-vapor region, pressure and temperature are linked by the saturation relation, so specifying both does not locate a unique mixture state. Another independent property, such as specific volume, is needed.

The state postulate is a counting rule, not an equation of state. It tells you how many independent properties are needed; constitutive relations or property data tell you their numerical relationships.