New Equation for Gas-Liquid/Solid Phase Transition

A new and concise equation for the gas-liquid or gas-solid phase transition is proposed based on the theory that the heat exchanges between a gas and its surroundings via the phase transition. Given that it is reversible, P=(1-x_2)RT/V_G and x_2=V_L/V_G e^(3/2-(π^α mg)/(RTV_G )). Similar to van der Waals’s equation for real gases, a factor of molecular interaction α is introduced in the form of system potential. Hence, it is also the state equation at saturation. P-V-T saturation data of 79 substances issued by the National Institute of Standards and Technology (NIST) are used as standards to calibrate the equation and determine α. As a result, the equation fits all substances well. The system potential is indispensable only near Tc in a narrow temperature region where the gas molar volume (VG) is comparable to the liquid (VL). It indicates that the system potential is achieved through short-term repulsive interactions rather than attractive ones. Tc corresponds to the temperature with a molar fraction of liquefaction x2 = 60-70%, at which the heat exchange is interrupted. α of each substance is determined by simulation. It seems to fall in the series: -2/3, -1/3, 0, 1/3, 2/3, 1, and 4/3.