Abstract

A system of mutually consistent equations for ethane is developed that describes pressure \({{p}_{s}}\), vapor density \({{\rho }^{ - }}\), liquid density \({{\rho }^{ + }}\), derivative \(p_{s}^{'}(T)\), and heat of vaporization \(r\) on the phase equilibrium line in the range of the triple point to the critical point. The system also includes apparent heat of vaporization \(r\text{*}\), which is associated with heat of vaporization \(r\): \(r = r\text{*}{\kern 1pt} (1 - {{\rho }^{ - }}{\text{/}}{{\rho }^{ + }})\). It is established on the basis of the thermodynamic analysis that (1) the condition of average diameter \({{d}_{f}} > 0\) is fulfilled at each point of the saturation line except for the critical point, at which \({{d}_{f}} = 0\), and (2) the average diameter is reduced sharply in the interval of \({{T}_{{{\text{tr}}}}} < T < {{T}_{c}}\). The system of mutually consistent equations reproduces the phase equilibrium line of ethane within the experimental uncertainty data of Funke et al. (2002) in the range of the triple point (\({{p}_{{{\text{tr}}}}}\), \({{\rho }_{{{\text{tr}}}}}\), \({{T}_{{{\text{tr}}}}}\)) to the critical point (\({{p}_{c}}\), \({{\rho }_{c}}\), \({{T}_{c}}\)). It also reproduces features of the critical point in accordance with the renormalization group (RG) theory developed by Zhou et al. (2022) for a system of asymmetric systems. Based on the Clausius–Clapeyron equation and renormalization group theory, an expression is obtained for the apparent heat of vaporization. Analysis of average diameter \({{d}_{f}} = {{D}_{{2\beta }}}{{\tau }^{{2\beta }}} + {{D}_{{1 - \alpha }}}{{\tau }^{{1 - \alpha }}} + {{D}_{\tau }}\tau \) for two groups of complexes shows that (a) \({{D}_{{2\beta }}} = 0.1\), \(\eta = {{D}_{{2\beta }}}{\text{/}}{{D}_{{1 - \alpha }}} = - 0.14\), and \(\phi = {{D}_{{2\beta }}}{\text{/}}{{D}_{\tau }} = 0.13\), and (b) \({{D}_{{2\beta }}} = 0.048\), \(\eta = - 0.18\), and \(\phi = 0.12\), which correspond to values \({{D}_{{2\beta }}}\), \(\eta \), and \(\phi \) obtained by Wang et al. (2013) in the RG theory and the modeling of experimental data for ethane on the saturation line. Based on the proposed system of mutually consistent equations, average diameter \({{d}_{f}}\)of ethane is found for complexes (a) and (b), and it is established that the average diameter determined on the basis of data by Funke et al. (2002) is given most accurately by the system of mutually consistent equations in the range of \({{T}_{{{\text{tr}}}}}\) to \({{T}_{c}}\) with parameters \({{D}_{{2\beta }}} = 0.0039\), \(\eta = - 0.14\), and \(\phi = 0.13\).

中文翻译：

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使用克拉佩龙-克劳修斯方程的重正化群理论中的乙烷饱和线

摘要

开发了一个相互一致的乙烷方程组，描述压力\({{p}_{s}}\)、蒸气密度\({{\rho }^{ - }}\)、液体密度\({{ \rho }^{ + }}\)、导数\(p_{s}^{'}(T)\)和三相点范围内相平衡线上的汽化热\(r\)临界点。该系统还包括表观汽化热\(r\text{*}\)，它与汽化热\(r\)相关：\(r = r\text{*}{\kern 1pt} (1 - {{\rho }^{ - }}{\text{/}}{{\rho }^{ + }})\)。根据热力学分析得出：（1）除临界点外，饱和线各点均满足平均直径\({{d}_{f}} > 0\)条件，在其中\({{d}_{f}} = 0\) ，并且 (2) 平均直径在\({{T}_{{{\text{tr}}}}}区间急剧减小< T < {{T}_{c}}\)。相互一致的方程组再现了 Funke 等人的实验不确定性数据中乙烷的相平衡线。(2002) 在三重点范围 ( \({{p}_{{{\text{tr}}}}}\) , \({{\rho }_{{{\text{tr}} }}}\) , \({{T}_{{{\text{tr}}}}}\) )到临界点 ( \({{p}_{c}}\) , \({ {\rho}_{c}}\) , \({{T}_{c}}\) )。它还根据 Zhou 等人提出的重整化群 (RG) 理论再现了临界点的特征。（2022）非对称系统的系统。基于克劳修斯-克拉佩龙方程和重正化群理论，得到了表观汽化热的表达式。平均直径分析\({{d}_{f}} = {{D}_{{2\beta }}}{{\tau }^{{2\beta }}} + {{D}_{两组复合体的{1 - \alpha }}}{{\tau }^{{1 - \alpha }}} + {{D}_{\tau }}\tau \) 表明 (a) \ ( {{D}_{{2\beta }}} = 0.1\) , \(\eta = {{D}_{{2\beta }}}{\text{/}}{{D}_{{ 1 - \alpha }}} = - 0.14\)，且\(\phi = {{D}_{{2\beta }}}{\text{/}}{{D}_{\tau }} = 0.13\)和 (b) \({{D}_{{2\beta }}} = 0.048\)、\(\eta = - 0.18\)和\(\phi = 0.12\)，分别对应到Wang 等人获得的值\({{D}_{{2\beta }}}\)、\(\eta \)和\(\phi \) 。(2013) RG 理论和乙烷饱和线实验数据建模。基于所提出的相互一致的方程组，平均直径\({{d}_{f}}\)发现了配合物(a)和(b)的乙烷，并且确定平均直径是根据Funke等人的数据确定的。(2002)由 \({{T}_{{{\text{tr}}}}}\)到\({{T}_{c}范围内的相互一致方程组最准确地给出}\)，参数为\({{D}_{{2\beta }}} = 0.0039\)、\(\eta = - 0.14\)和\(\phi = 0.13\)。