,

where is the universal gas constant, is the constant-pressure heat capacity and is the compressibility factor. In order to estimate the value of , two equations of state are applied: the Soave–Redlich–Kwong (SRK) EoS and the Peng–Robinson (PR) EoS.

This Demonstration uses arc-length continuation to compute the Joule–Thomson inversion curve (i.e. the loci of the points, in the - plane, where ). Here we choose propylene, but the program can be modified for any other pure component. You can set the value of the reduced pressure and temperature (i.e. and , respectively). This Demonstration will mark your choice by a green dot in the - plane. If your choice corresponds to a point inside the colored area, then the value of the Joule–Thomson coefficient is positive (see Snapshot 1); otherwise (see Snapshot 2). The inversion curve and colored region are both indicated either in red (for the SRK EoS) or in blue (for the PR EoS).