Modified Van Der Waals Equation And Gas-Liquid Coexistence Line

It is well known that the Van der Waals equation is a modification of the ideal gas law, yet it can be used to describe both gas and liquid, and some important messages can be obtained from this state equation.However, the Van der Waals equation is not a precise state equation, and it does not give a good description of the law of corresponding states. In this paper, we expand the Van der Waals equation into its Taylor’s series form, and then modify the fourth order expansion by changing the constant coefficients into the adjustable coefficients. In this way, a more precise result about the law of corresponding states has been obtained,furthermore the law of corresponding states can be expressed as: in terms of the reduced variables, all fluids should obey the same equation with variable coefficients. Though our result seems better than that of many phenomenological state equations, the deeper physics intrinsic on the modification of Van der Waals equation still needs more research.Meanwhile it is found that the realation betweeb the parameter introduced to modify the Van der Waals equation and the density is exponential.In addition, the quantum effect of the corresponding state is also taken into consideration. By comparing the results of the Van der Waals equation and the results of experimental, including Helium 3 and Helium4, a new factor, which is larger than 1, is introduced in the equation of state, and the coexistence line of this modified equation is obtained. It isfound that they are in good agreement to the experimental results.Furthermore, we note that, for a normal system without quantum effect,the modification of the Van der Waals equation is larger than the real case,however, for a normal system with quantum effect, the modification of the Van der Waals equation is smaller than the real case, that is why the modifactor is introduced in this paper to decrease or increase the modification of the Van der Waals equation.