Thermal Heat Capacity Equation Formula Latex Code and Summary

Thermal Heat Capacity

Tags: #physics #thermodynamics #heat capacity

Equation

$$C_p-C_V=T\left(\frac{\partial p}{\partial T}\right)_{V}\cdot\left(\frac{\partial V}{\partial T}\right)_{p}=-T\left(\frac{\partial V}{\partial T}\right)_{p}^2\left(\frac{\partial p}{\partial V}\right)_{T}\geq0 \\ \displaystyle C_X=T\left(\frac{\partial S}{\partial T}\right)_{X} \\ \displaystyle C_p=\left(\frac{\partial H}{\partial T}\right)_{p} \\ \displaystyle C_V=\left(\frac{\partial U}{\partial T}\right)_{V} \\ C_{mp}-C_{mV}=R$$

Latex Code

                                 C_p-C_V=T\left(\frac{\partial p}{\partial T}\right)_{V}\cdot\left(\frac{\partial V}{\partial T}\right)_{p}=-T\left(\frac{\partial V}{\partial T}\right)_{p}^2\left(\frac{\partial p}{\partial V}\right)_{T}\geq0 \\
            \displaystyle C_X=T\left(\frac{\partial S}{\partial T}\right)_{X} \\
            \displaystyle C_p=\left(\frac{\partial H}{\partial T}\right)_{p} \\
            \displaystyle C_V=\left(\frac{\partial U}{\partial T}\right)_{V} \\
            C_{mp}-C_{mV}=R

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Introduction

$C_p-C_V=T\left(\frac{\partial p}{\partial T}\right)_{V}\cdot\left(\frac{\partial V}{\partial T}\right)_{p}=-T\left(\frac{\partial V}{\partial T}\right)_{p}^2\left(\frac{\partial p}{\partial V}\right)_{T}\geq0 \\ \displaystyle C_X=T\left(\frac{\partial S}{\partial T}\right)_{X} \\ \displaystyle C_p=\left(\frac{\partial H}{\partial T}\right)_{p} \\ \displaystyle C_V=\left(\frac{\partial U}{\partial T}\right)_{V} \\ C_{mp}-C_{mV}=R$

Latex Code

            C_p-C_V=T\left(\frac{\partial p}{\partial T}\right)_{V}\cdot\left(\frac{\partial V}{\partial T}\right)_{p}=-T\left(\frac{\partial V}{\partial T}\right)_{p}^2\left(\frac{\partial p}{\partial V}\right)_{T}\geq0 \\
            \displaystyle C_X=T\left(\frac{\partial S}{\partial T}\right)_{X} \\
            \displaystyle C_p=\left(\frac{\partial H}{\partial T}\right)_{p} \\
            \displaystyle C_V=\left(\frac{\partial U}{\partial T}\right)_{V} \\
            C_{mp}-C_{mV}=R

Explanation

Latex code for the Thermodynamics Introduction. I will briefly introduce the notations in this formulation.

$\displaystyle C_X=T\left(\frac{\partial S}{\partial T}\right)_{X}$ : The specific heat at constant at X
$\displaystyle C_p=\left(\frac{\partial H}{\partial T}\right)_{p}$ : The specific heat at constant pressure
$\displaystyle C_V=\left(\frac{\partial U}{\partial T}\right)_{V}$ : The specific heat at constant volume

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