Two-Phase Isochoric Heat Capacity, Phase Transition, and Theoretically Important Physical Parameters of Methyl Dodecanoate

Abstract

The two-phase isochoric heat capacity (\(C_{{\text{V2}}}\) VT), liquid–gas phase transition (\(T_{\text{S}}\),\(\rho_{{\text{s}}}^{\prime }\)), vapor-pressure (\(P_{{\text{S}}}\),\(T_{\text{S}}\)), and thermal -pressure coefficient \(\left( {dP_{\text{S}} /dT} \right)\) of methyl dodecanoate, a key biofuels component, have been measured along nine liquid isochores between (180.90 and 845.31) kg·m⁻³ and three near-critical liquid and vapor (180.90, 234.52, and 374.11) kg·m⁻³ isochores. The temperature range covers the liquid–vapor phase transition temperature \(T_{\text{S}} \left( \rho \right)\) for each measured isochore to near the thermal decomposition temperature, 450 K. The measurements were performed using a high-temperature and high-pressure, nearly constant-volume adiabatic calorimeter previously used for the measurements of the \(C_{\text{V}}\) VT relationship of biofuel components in the two- and single-phase region. The combined expanded uncertainty of the density (ρ), temperature (T), and isochoric heat capacity (\(C_{{\text{V2}}}\)) measurements at the 95% confidence level with a coverage factor of k = 2 is estimated to be 0.15%, 15 mK, and 2%, respectively. The isochoric heat capacity discontinuity point was used as the criteria of the liquid–gas phase transition temperature, \(T_{{\text{S}}}\). For each experimental liquid isochore, most measurements were concentrated in the immediate vicinity of the liquid–gas phase transition temperature (\(T_{{\text{S}}}\)) to precisely determine the phase boundary properties (\(\rho_{{\text{S}}}\), \(T_{{\text{S}}}\), \(C_{\text{V1}}\), and \(C_{\text{V2}}\)) using an isochoric heat -capacity abrupt-behavior technique. For nine liquid isochores between (745.16 and 845.31) kg·m⁻³ the phase transition temperatures (\(T_{{\text{S}}}\)) were experimentally determined. For two vapor (180.90 and 234.52) kg·m⁻³ and liquid near-critical (374.11) kg·m⁻³ isochores, for which the transition temperatures are very high (above the thermal decomposition temperature, 473 K), we failed to reach the phase-transition temperatures, \(T_{{\text{S}}}\), because for these isochores the thermal decomposition of methyl dodecanoate occurs before reaching the phase transition temperature (above 673 K). The measured two-phase (\(C_{\text{V2}}\)) isochoric heat capacities as a function of specific volume (V) along the various isotherms (below 473 K) were used to accurately estimate the values of the second temperature derivatives of chemical potential, \(\frac{{{\text{d}}^{{2}} \mu }}{{{\text{d}}T^{2} }}\), and vapour-pressure,\(\frac{{{\text{d}}^{2} P_{{\text{S}}} }}{{{\text{d}}T^{2} }}\), based on the Yang–Yang theoretical relation. The contributions of the vapour-pressure,\(C_{{{\text{VP}}}} = VT\frac{{{\text{d}}^{2} P_{{\text{S}}} }}{{{\text{d}}T^{2} }}\), and the chemical potential, \(C_{{{\text{V}}\mu }} = - T\frac{{{\text{d}}^{{\text{2}}} \mu }}{{{\text{d}}T^{2} }}\), to the heat capacities of the measured total two-phase \(C_{\text{V2}}\) were estimated as a function of temperature. In addition, measured \(C_{\text{V2}}\) and phase boundary (\(\rho_{{\text{S}}}\),\(T_{{\text{S}}}\),\(P_{{\text{S}}}\)) property data were used to calculate key thermodynamic property data \(C_{{\text{P}}}\),\(C_{\text{sat}}\),\(K_{\text{TS}}\),\(W_{\text{S}}\),\(\Delta H_{{\text{V}}}\),\(\left( {\frac{\partial P}{{\partial T}}} \right)_{{\text{V}}}^{{{\text{sat}}{.}}}\),\(\left( {\frac{{\partial V}}{{\partial T}}} \right)_{{\text{P}}}^{{{\text{sat}}.}}\) along the saturation curve. The measured vapor-pressure (\(P_{{\text{S}}}\) − \(T_{{\text{S}}}\)) and saturated liquid densities (\(\rho_{{\text{S}}}\) − \(T_{{\text{S}}}\)) were used to develop extended theoretically based scaling -type correlations and to estimate the critical property data (\(T_{{\text{C}}}\), \(P_{{\text{C}}}\), and \(\rho_{{\text{C}}}\)), asymptotical critical amplitudes, and asymmetric parameter.