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Statistical Mechanics

Partition function

Partition Function

Number of States and Probabilities

Energy Distribution

Energy Distribution

Storyboard

The partition function not only allows calculating the average value of energy, it also allows determining the mean value of the square and thus the standard deviation of the probability of energy.

ID:(1570, 0)

Energy Distribution

Model

The partition function not only allows calculating the average value of energy, it also allows determining the mean value of the square and thus the standard deviation of the probability of energy.

Variables

Symbol

Text

Variable

Value

Units

Calculate

MKS Value

MKS Units

$\beta$

beta

Beta del sistema

1/J

$\overline{(\Delta E)^2}$

DE2

Desviación de la energía al cuadrado

J^2

$E_r$

E_r

Energía del estado $r$

J

$Z$

Z

Función Partición

-

$r$

r

Numero del estado

-

$\bar{E^2}$

mE2

Promedio de la energía al cuadrado

J^2

Calculations

Equation

Number

First, select the equation:

to

, then, select the variable:

to

Symbol

Equation

Solved

Translated

Calculations

Symbol

Equation

Solved

Translated

Variable

Given

Calculate

Target :

Equation

To be used

Equations

$\overline{E^2}=\displaystyle\frac{1}{Z}\displaystyle\frac{\partial^2Z}{\partial\beta^2}$

E^2=(1/Z)*(d^2Z/dbeta^2)

(ID 3529)

$\overline{(\Delta E)^2}=\displaystyle\frac{\partial^2\ln Z}{\partial\beta^2}$

DE^2=d^2ln Z/dbeta^2

(ID 3530)

$\bar{E^2}=\displaystyle\frac{\displaystyle\sum_rE_r^2e^{-\beta E_r}}{\displaystyle\sum_re^{-\beta E_r}}$

E^2=sum_rE_r^2*e^(-beta*E_r)/sum_re^(-beta*E_r)

(ID 11617)

Examples

ID:(1570, 0)