Phase Transitions Equation Formula Latex Code and Summary

Phase Transitions

Tags: #physics #thermodynamics #phase transitions

Equation

$$\Delta S_m=S_m^\alpha - S_m^\beta=\frac{r_{\beta\alpha}}{T_0} \\ S_m=\left(\frac{\partial G_m}{\partial T}\right)_{p} \\ \frac{dp}{dT}=\frac{S_m^\alpha-S_m^\beta}{V_m^\alpha-V_m^\beta}= \frac{r_{\beta\alpha}}{(V_m^\alpha-V_m^\beta)T} \\ p=p_0{\rm e}^{-r_{\beta\alpha/RT}} \\ r_{\beta\alpha}=r_{\alpha\beta} \\ r_{\beta\alpha}=r_{\gamma\alpha}-r_{\gamma\beta} \\ \frac{dp}{dT}=\frac{S_m^\alpha-S_m^\beta}{V_m^\alpha-V_m^\beta}= \frac{r_{\beta\alpha}}{(V_m^\alpha-V_m^\beta)T} \\ p=p_0{\rm e}^{-r_{\beta\alpha/RT}}$$

Latex Code

                                 \Delta S_m=S_m^\alpha - S_m^\beta=\frac{r_{\beta\alpha}}{T_0} \\
            S_m=\left(\frac{\partial G_m}{\partial T}\right)_{p} \\
            \frac{dp}{dT}=\frac{S_m^\alpha-S_m^\beta}{V_m^\alpha-V_m^\beta}= \frac{r_{\beta\alpha}}{(V_m^\alpha-V_m^\beta)T} \\
            p=p_0{\rm e}^{-r_{\beta\alpha/RT}} \\
            r_{\beta\alpha}=r_{\alpha\beta} \\
            r_{\beta\alpha}=r_{\gamma\alpha}-r_{\gamma\beta} \\
            \frac{dp}{dT}=\frac{S_m^\alpha-S_m^\beta}{V_m^\alpha-V_m^\beta}= \frac{r_{\beta\alpha}}{(V_m^\alpha-V_m^\beta)T} \\
            p=p_0{\rm e}^{-r_{\beta\alpha/RT}}

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Introduction

$\Delta S_m=S_m^\alpha - S_m^\beta=\frac{r_{\beta\alpha}}{T_0} \\ S_m=\left(\frac{\partial G_m}{\partial T}\right)_{p} \\ \frac{dp}{dT}=\frac{S_m^\alpha-S_m^\beta}{V_m^\alpha-V_m^\beta}= \frac{r_{\beta\alpha}}{(V_m^\alpha-V_m^\beta)T} \\ p=p_0{\rm e}^{-r_{\beta\alpha/RT}}$

Latex Code

            \Delta S_m=S_m^\alpha - S_m^\beta=\frac{r_{\beta\alpha}}{T_0} \\
            S_m=\left(\frac{\partial G_m}{\partial T}\right)_{p} \\
            \frac{dp}{dT}=\frac{S_m^\alpha-S_m^\beta}{V_m^\alpha-V_m^\beta}= \frac{r_{\beta\alpha}}{(V_m^\alpha-V_m^\beta)T} \\
            p=p_0{\rm e}^{-r_{\beta\alpha/RT}} \\
            r_{\beta\alpha}=r_{\alpha\beta} \\
            r_{\beta\alpha}=r_{\gamma\alpha}-r_{\gamma\beta} \\
            \frac{dp}{dT}=\frac{S_m^\alpha-S_m^\beta}{V_m^\alpha-V_m^\beta}= \frac{r_{\beta\alpha}}{(V_m^\alpha-V_m^\beta)T} \\
            p=p_0{\rm e}^{-r_{\beta\alpha/RT}}

Explanation

Latex code for the Phase Transitions. Phase transitions are isothermal and isobaric. I will briefly introduce the notations in this formulation.

$p$ : ideal gas one finds for the vapor line at some distance from the critical point.

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