Thermodynamics Definitions
Tags: #physics #thermodynamicsEquation
$$f(x,y,z)=0 \\ dz=\left(\frac{\partial z}{\partial x}\right)_{y}dx+\left(\frac{\partial z}{\partial y}\right)_{x}dy \\ \left(\frac{\partial x}{\partial y}\right)_{z}\cdot\left(\frac{\partial y}{\partial z}\right)_{x}\cdot\left(\frac{\partial z}{\partial x}\right)_{y}=-1 \\ \varepsilon^m F(x,y,z)=F(\varepsilon x,\varepsilon y,\varepsilon z) \\ mF(x,y,z)=x\frac{\partial F}{\partial x}+y\frac{\partial F}{\partial y}+z\frac{\partial F}{\partial z}$$Latex Code
f(x,y,z)=0 \\
dz=\left(\frac{\partial z}{\partial x}\right)_{y}dx+\left(\frac{\partial z}{\partial y}\right)_{x}dy \\
\left(\frac{\partial x}{\partial y}\right)_{z}\cdot\left(\frac{\partial y}{\partial z}\right)_{x}\cdot\left(\frac{\partial z}{\partial x}\right)_{y}=-1 \\
\varepsilon^m F(x,y,z)=F(\varepsilon x,\varepsilon y,\varepsilon z) \\
mF(x,y,z)=x\frac{\partial F}{\partial x}+y\frac{\partial F}{\partial y}+z\frac{\partial F}{\partial z}
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Introduction
Equation
Latex Code
f(x,y,z)=0 \\
dz=\left(\frac{\partial z}{\partial x}\right)_{y}dx+\left(\frac{\partial z}{\partial y}\right)_{x}dy \\
\left(\frac{\partial x}{\partial y}\right)_{z}\cdot\left(\frac{\partial y}{\partial z}\right)_{x}\cdot\left(\frac{\partial z}{\partial x}\right)_{y}=-1 \\
\varepsilon^m F(x,y,z)=F(\varepsilon x,\varepsilon y,\varepsilon z) \\
mF(x,y,z)=x\frac{\partial F}{\partial x}+y\frac{\partial F}{\partial y}+z\frac{\partial F}{\partial z}
Explanation
Latex code for the Thermodynamics Introduction. I will briefly introduce the notations in this formulation.
: The total differential dz
A homogeneous function of degree m
: The isochoric pressure coefficient
: The isothermal compressibility
: The isobaric volume coefficient
: The adiabatic compressibility
: The ideal gas follows
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