凡得瓦方程式之研究

Abstract

本論文把凡得瓦方程式的歷史淵源作一個有系統的交代，以代數方法及相關熱力學理論探討了方程式的內涵，比較了幾種氣體的臨界溫度之實驗值與理論值。並以水蒸氣、氮氣、二氧化碳等氣體，實際考察凡得瓦方程式對相變化的描述，運用馬克士威的等面積法則於有起伏的等溫曲線上，得到結果顯示: 一、對不同種類分子，凡得瓦方程式所得之數據與實測數據並不都能符合良好，水蒸氣與二氧化碳的飽和蒸氣壓值就有正偏差與負偏差，蓋因各種不同氣體分子的形狀及它們之間的作用力變化相當複雜，以致分子間位能之型態不盡然相同。 二、在略低於臨界溫度時，凡得瓦方程在定量上尚能符合實驗數據，但在溫度更低時，與實驗數據差異頗大。我們若改用後來提出的R-K方程畫等溫線再以同樣方法比對所得之數據，比凡得瓦方程所得者更接近實驗數據。

This thesis aims to make a clear and systematic explaination of the historical origins of van der waals equation, explore the connotation of van der waals equation with algebraic methods and related thermodynamic theory. We compared the experimental and theoretical values of the critical temperature of the several gas,including water vapor, nitrogen,carbon dioxide,and examined the application of van der Waals equation to phase transition phenomena. When the method of Maxwell's Construction is applied to the Van der Waals isotherm, the following conclusions are obtained: (1) The theoretical values of the vapor pressure of the different gas molecules obtained by the van der Waals equation is not completely in accordance with the experimental values, there is a positive deviation of the saturated vapor pressure of water vapor, and carbon dioxide value shows a negative deviation. The reason is the structure of the various gas molecules are quite different, so the intermolecular potential varies drastically. (2) When the temperature is only slightly lower than the critical temperature, the theoretical value can still fit the experimental data. Well, however, for still lower temperatures, the difference between the two is significant. When we switch to an R-K equation and do the same type of comparison, the difference between the theoretical value and experimental data is reduced.