Thermodynamic Potential Equation Formula Latex Code and Summary

Thermodynamic Potential

Tags: #physics #thermodynamics

Equation

$$dG=-SdT+Vdp+\sum_i\mu_idn_i \\ \displaystyle\mu=\left(\frac{\partial G}{\partial n_i}\right)_{p,T,n_j} \\ V=\sum_{i=1}^c n_i\left(\frac{\partial V}{\partial n_i}\right)_{n_j,p,T}:=\sum_{i=1}^c n_i V_i \\ \begin{aligned} V_m&=&\sum_i x_i V_i\\ 0&=&\sum_i x_i dV_i\end{aligned}$$

Latex Code

                                 dG=-SdT+Vdp+\sum_i\mu_idn_i \\
            \displaystyle\mu=\left(\frac{\partial G}{\partial n_i}\right)_{p,T,n_j} \\
            V=\sum_{i=1}^c n_i\left(\frac{\partial V}{\partial n_i}\right)_{n_j,p,T}:=\sum_{i=1}^c n_i V_i \\
            \begin{aligned} V_m&=&\sum_i x_i V_i\\ 0&=&\sum_i x_i dV_i\end{aligned}

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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

            dG=-SdT+Vdp+\sum_i\mu_idn_i \\
            \displaystyle\mu=\left(\frac{\partial G}{\partial n_i}\right)_{p,T,n_j} \\
            V=\sum_{i=1}^c n_i\left(\frac{\partial V}{\partial n_i}\right)_{n_j,p,T}:=\sum_{i=1}^c n_i V_i \\
            \begin{aligned} V_m&=&\sum_i x_i V_i\\ 0&=&\sum_i x_i dV_i\end{aligned}

Explanation

Latex code for the Thermodynamic Potential. I will briefly introduce the notations in this formulation.

$\displaystyle\mu=\left(\frac{\partial G}{\partial n_i}\right)_{p,T,n_j}$ : thermodynamic potential.
$V_i$ : partial volume of component i.

Discussion

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Janice Reed

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2023-01-17 00:00
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You can make it...

2023-02-03 00:00:00.0
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Daniel Anderson

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2023-10-21 00:00
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Chris Burton reply to Daniel Anderson

Nice~

2023-11-19 00:00:00.0
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Stephanie Robinson

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2023-09-13 00:00
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Steven Harris reply to Stephanie Robinson

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2023-09-17 00:00:00.0
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