Relation between Isotherms and Coexistence Curve in the Critical Region

摘要

A general relation has been given relating the slope of the isotherms along the liquidhyphen;vapor coexistence curve to the shape of the latter, and has been applied to the case where the coexistence curve is rounded on the top and to the case where it has a flat horizontal portion. If the coexistence curve has the formTmdash;Tc= mdash;averbar;rgr;cmdash;rgr;verbar;n(whereT= temperature, rgr;=density, subscriptcindicates a value at the critical point, andaandnare constants) it can be shown that the critical isotherm is given byPminus;Pcequals;alpar;part;2Psol;part;Tpart;rgr;rpar;clpar;rgr;minus;rgr;crpar;verbar;rgr;minus;rgr;cverbar;n,provided (part;2P/part;Tpart;rgr;)cis finite. This equation should hold over the region where part;2P/part;Tpart;rgr; is approximately constant. If there is a flat, horizontal portion at the top of the isotherm a similar equation will be approximately true under the same conditions beyond the flat portion. The actual shape of experimental isotherms in the critical region is considered. part;2P/part;Tpart;rgr; is approximately constant only over a limited range of densities, and beyond this range the slopes of the isotherms become greater than indicated by the equation; however, general orders of magnitude are as expected. It is not possible to decide definitely from the data considered whether the critical isotherm has a horizontal region over a finite range of densities. Finally, a discussion is given of the discontinuities of thermodynamic quantities, particularlyCv,as one passes from the onehyphen;phase to the twohyphen;phase region. It is shown thatCvmust be much larger in the twohyphen;phase than in the onehyphen;phase region.