Thermal Heat Capacity
Tags: #physics #thermodynamics #heat capacityEquation
$$C_p-C_V=T\left(\frac{\partial p}{\partial T}\right)_{V}\cdot\left(\frac{\partial V}{\partial T}\right)_{p}=-T\left(\frac{\partial V}{\partial T}\right)_{p}^2\left(\frac{\partial p}{\partial V}\right)_{T}\geq0 \\ \displaystyle C_X=T\left(\frac{\partial S}{\partial T}\right)_{X} \\ \displaystyle C_p=\left(\frac{\partial H}{\partial T}\right)_{p} \\ \displaystyle C_V=\left(\frac{\partial U}{\partial T}\right)_{V} \\ C_{mp}-C_{mV}=R$$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
Equation
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.
: The specific heat at constant at X
: The specific heat at constant pressure
: The specific heat at constant volume
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