The Yang-Yang relation and the specific heats of propane and carbon dioxide

The Yang-Yang relation expresses the heat capacity at constant volume, C-V( T,rho), of a fluid linearly in terms of the second temperature derivatives of the pressure and the chemical potential, p double prime>(*) over bar * ( T,rho) and mu double prime>(*) over bar * (T,rho). At a gas-liquid critical point C-V diverges so, on approaching T-c from below, either p(sigma)doubl e prime>(*) over bar * (T), or mu (sigma)double prime>(*) over bar * (T), o r both must diverge, where the subscript sigma denotes the evaluation of p and mu on the phase boundary or vapor-pressure curve. However, previous the oretical and experimental studies have suggested that mu (sigma)double prim e>(*) over bar * (T) always remains finite. To test these inferences, we pr esent an analysis of extensive two-phase heat capacity data for propane rec ently published by Abdulagatov and co-workers. By careful interpolation in temperature and subsequently making linear, isothermal fits vs specific vol ume and vs density, we establish that the divergence is shared almost equal ly between the derivatives p(sigma)double prime>(*) over bar * (T) and mu ( sigma)double prime>(*) over bar * (T). A re-examination of the analysis of Gaddy and White for carbon dioxide leads to similar conclusions although th e singular contribution from mu (sigma)double prime>(*) over bar * (T) is f ound to be of opposite sign and probably somewhat smaller than in propane. (C) 2000 American Institute of Physics. [S0021-9606(00)50339-0].