T-\nu and P-\nu Diagrams
A pure substance has a homogeneous composition, and can exist as a mixture of different phases. The phase of a substance is dependent on the pressure, density, and temperature of the substance. Because the phase of a substance is defined by these three properties we can plot them against each other, commonly temperature/pressure vs specific volume.
It can be observed that there is a certain specific volume, \nu_f, where the temperature stays constant, this is the point at which a liquid begins to boil and transition into a gas. Temperature starts to rise again at a higher specific volume, \nu_g, where the fluid has become entirely gaseous. It is common to use the value \nu_{fg} to denote the change in specific volume between \nu_f and \nu_g (\nu_{fg}=\nu_g-\nu_f). By plotting every \nu_f and \nu_g for various pressures we obtain a more comprehensive view of the states of a substance under different conditions.
The phase of a substance can be determined by comparing the conditions with the saturation temperature/pressure/specific volume. The saturation values are the temperature/pressure values held constant within the saturated mixture region for temperature/pressure, and \nu_f/\nu_g for specific volume.
Criteria used to determine phase of substance
| Phase | P | T | \nu |
|---|---|---|---|
| Compressed Liquid | P>P_{sat} | T < T_{sat} | \nu < \nu_f |
| Saturated Mixture | P=P_{sat} | T=T_{sat} | \nu_f < \nu < \nu_g |
| Superheated Vapour | P < P_{sat} | T>T_{sat} | \nu>\nu_g |
Compressed Liquids
In the compressed liquid region the entire substance is liquid, and \nu is solely a function of temperature. As a result, the specific volume for a compressed liquid at a specific temperature will be approximated by the saturated liquid specific volume at the same temperature, i.e.
\nu(T)\approx\nu_f (T)
Saturated Mixtures
In the saturated mixture region the substance is partially liquid and partially gaseous. This region lies between the saturated liquid and saturated vapour lines, \nu_f and \nu_g at a given pressure/temperature. Quality, x, determines how much of the substance is liquid/gas. Quality is formally defined as the ratio of gaseous mass to the total mass of the substance:
x=\dfrac{m_g}{m}
The quality of the substance can be expressed in terms of specific volume:
\nu=(1-x)\nu_f+x\nu_g
\nu=x\nu_{fg}+\nu_f
Superheated Vapours
In the saturated vapour region the entire substance is gaseous and quality is indeterminate. Tables exist tabulating the properties of superheated vapours.
Ideal Gases
Ideal gases are formed at pressures far below the substance critical pressure and at high temperatures, over twice as high as the substance critical temperature. The ideal gas law relates the pressure, temperature, mass, and volume of a substance with a constant, the universal gas constant, \overline{R}=8.3145\frac{\text{kJ}}{\text{kmolK}}.
PV=n\overline{R}T
The universal gas constant can be normalized using the molar mass, M of each substance, as such each substance has a unique ideal gas constant, R=\dfrac{\overline{R}}{M}. The ideal gas law can therefore also be written for a specific substance:\dfrac{P\nu}{T}=R
PV=mRT