Thermodynamics Statistical Basis
Tags: #physics #thermodynamicsEquation
$$P=N!\prod_i\frac{g_i^{n_i}}{n_i!} \\ n_i=\frac{N}{Z}g_i\exp\left(-\frac{W_i}{kT}\right) \\ Z=\sum\limits_ig_i\exp(-W_i/kT) \\ Z=\frac{V(2\pi mkT)^{3/2}}{h^3} \\ \text{Entropy in Thermodynamic Equilibrium} \\ S=\frac{U}{T}+kN\ln\left(\frac{Z}{N}\right)+kN\approx\frac{U}{T}+k\ln\left(\frac{Z^N}{N!}\right) \\ \text{Ideal gas} \\ S=kN+kN\ln\left(\frac{V(2\pi mkT)^{3/2}}{Nh^3}\right)$$Latex Code
P=N!\prod_i\frac{g_i^{n_i}}{n_i!} \\
n_i=\frac{N}{Z}g_i\exp\left(-\frac{W_i}{kT}\right) \\
Z=\sum\limits_ig_i\exp(-W_i/kT) \\
Z=\frac{V(2\pi mkT)^{3/2}}{h^3} \\
\text{Entropy in Thermodynamic Equilibrium} \\
S=\frac{U}{T}+kN\ln\left(\frac{Z}{N}\right)+kN\approx\frac{U}{T}+k\ln\left(\frac{Z^N}{N!}\right) \\
\text{Ideal gas} \\
S=kN+kN\ln\left(\frac{V(2\pi mkT)^{3/2}}{Nh^3}\right)
Have Fun
Let's Vote for the Most Difficult Equation!
Introduction
Equation
Latex Code
P=N!\prod_i\frac{g_i^{n_i}}{n_i!} \\
n_i=\frac{N}{Z}g_i\exp\left(-\frac{W_i}{kT}\right) \\
Z=\sum\limits_ig_i\exp(-W_i/kT) \\
Z=\frac{V(2\pi mkT)^{3/2}}{h^3} \\
\text{Entropy in Thermodynamic Equilibrium} \\
S=\frac{U}{T}+kN\ln\left(\frac{Z}{N}\right)+kN\approx\frac{U}{T}+k\ln\left(\frac{Z^N}{N!}\right) \\
\text{Ideal gas} \\
S=kN+kN\ln\left(\frac{V(2\pi mkT)^{3/2}}{Nh^3}\right)
Explanation
Latex code for the Thermodynamics Statistical Basis. I will briefly introduce the notations in this formulation.
: number of possibilities
: number of particles
: number of possible energy levels
: g-fold degeneracy
: The occupation numbers in equilibrium(with the maximum value for P)
: State sum Z is a normalization constant
: one component in a second gives rise to decrease of the freezing point
Reply