Thermodynamics Definitions

Tags: #physics #thermodynamics

Equation

f (x, y, z) = 0 d z = {(\frac{\partial z}{\partial x})}_{y} d x + {(\frac{\partial z}{\partial y})}_{x} d y {(\frac{\partial x}{\partial y})}_{z} \cdot {(\frac{\partial y}{\partial z})}_{x} \cdot {(\frac{\partial z}{\partial x})}_{y} = - 1 ε^{m} F (x, y, z) = F (ε x, ε y, ε z) m F (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}

Have Fun

Let's Vote for the Most Difficult Equation!

Introduction

$f(x,y,z)=0 \\ dz=\left(\frac{\partial z}{\partial x}\right)_{y}dx+\left(\frac{\partial z}{\partial y}\right)_{x}dy \\ \left(\frac{\partial x}{\partial y}\right)_{z}\cdot\left(\frac{\partial y}{\partial z}\right)_{x}\cdot\left(\frac{\partial z}{\partial x}\right)_{y}=-1 \\ \varepsilon^m F(x,y,z)=F(\varepsilon x,\varepsilon y,\varepsilon z) \\ mF(x,y,z)=x\frac{\partial F}{\partial x}+y\frac{\partial F}{\partial y}+z\frac{\partial F}{\partial z}$

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}

Explanation

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

$dz$ : The total differential dz
$\varepsilon^m F(x,y,z)=F(\varepsilon x,\varepsilon y,\varepsilon z)$ A homogeneous function of degree m
$\displaystyle \beta_V=\frac{1}{p}\left(\frac{\partial p}{\partial T}\right)_{V}$ : The isochoric pressure coefficient
$\displaystyle \kappa_T=-\frac{1}{V}\left(\frac{\partial V}{\partial p}\right)_{T}$ : The isothermal compressibility
$\displaystyle \gamma_p=\frac{1}{V}\left(\frac{\partial V}{\partial T}\right)_{p}$ : The isobaric volume coefficient
$\displaystyle \kappa_S=-\frac{1}{V}\left(\frac{\partial V}{\partial p}\right)_{S}$ : The adiabatic compressibility
$\gamma_p=1/T, \kappa_T=1/p, \beta_V=-1/V$ : The ideal gas follows

Comments

Brian Clark 2023-12-08 00:00

Passing this test is crucial for me.

0

0

Follow

Reply

Barbara Garcia

replies to

Brian Clark

2024-01-06 00:00

Best Wishes.

Reply
Brent Shaw 2023-05-16 00:00

I've been dreaming of passing this exam.

0

0

Follow

Reply

Jane Howard

replies to

Brent Shaw

2023-06-14 00:00

Gooood Luck, Man!

Reply
Maria Stewart 2024-02-06 00:00

I'm aiming for a successful outcome on this exam.

0

0

Follow

Reply

Gerald Diaz

replies to

Maria Stewart

2024-02-16 00:00

Nice~

Reply

Write Your Comment

Chatbot close

Bot
Hi there
How can I help you today?

Send

Thermodynamics Definitions

Equation

Latex Code

Have Fun

Introduction

Equation

Latex Code

Explanation

Related Documents

Related Videos

Comments

Write Your Comment