A simple compressible system entails a single substance in a container of variable volume, and may be visualized as water contained by a piston. The substance can experience heat transfer through the container, and work may be done on the substance by variation of the container’s volume.
Liquid-vapor mixture of water in a simple compressible system
The state principle says that
For a simple compressible system, the values of any two independent intensive properties specify the state.
In other words, if we know the value of two independent intensive properties, such as specific volume and temperature, we can determine the exact state of the system and can find any other property, such as pressure.
Pressure, Specific Volume, and Temperature are three properties frequently used to specify a thermodynamic state. The relationship between these three quantities is illustrated below by the $p-v-T$ surface for water.
The $p-v-T$ values for which water is solid are shown in purple, liquid in dark blue, and gas in cyan. The actual values of this surface are summarized in lookup tables. The critical thing to notice in this illustration is the vapor dome, the parabola-like region in which water is a saturated liquid-vapor mixture. At the curved edges of the vapor dome, the substance is either a saturated liquid or a saturated vapor, depending on the side.
Within the vapor dome, the pressure and temperature do not vary with respect to the specific volume. Recall from chemistry how a liquid stalls temperature while boiling, such that the pressure and temperature are constant throughout the boiling, but the specific volume changes as the percentage of the mass which is gaseous increases. Because of this phenomenon, for liquid-vapor mixtures, pressure and temperature are not independent, and are insufficient to specify the state of the system. Rather, we need a different property, such as specific volume, to specify the state.
Quality is the mass-wise portion of the substance in a gaseous phase. It can be obtained from reference tables using any intensive quantity, $a$, in pair with pressure or temperature. The pressure or temperature are used to determine the value of the intensive quantity for a saturated vapor, $a_g$, and saturated liquid, $a_f$. Quality may then be used to calculate any intensive property.
$$ x=\frac{m_g}{m_f+m_g}=\frac{a-a_f}{a_g-a_f}\Rarr b=(1-x)b_f+(x)b_g $$
It is also notable that it is projections of the $p,v,T$ surface that give us other useful thermodynamic diagrams. These are the state diagram $(p, T)$, the $(p,v)$ diagram, and the $(T, v)$ diagram.