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Macrocanonical Partition Function

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>Model

ID:(473, 0)

Macrocanonical Partition Function

Description

Variables

Symbol

Text

Variable

Value

Units

Calculate

MKS Value

MKS Units

$\beta$

beta

Beta

1/J

$E_r$

E_r

Energía del estado

$r$

$U$

Energía interna

$\alpha$

alpha

Factor alpha

$\cal Z$

Función partición distribución gran-canónica

$N$

Numero de partículas

$r$

Numero del estado

$r$

$\bar{N}$

Numero medio de partículas

Calculations

Equation

Number

First, select the equation:

, then, select the variable:

Symbol

Equation

Solved

Translated

Calculations

Symbol

Equation

Solved

Translated

Variable

Given

Calculate

Target :

Equation

To be used

Equations

$Z=\displaystyle\sum_Re^{-\beta E_R}$

Z=sum_Re^(-beta*E_R)

(ID 3527)

$\bar{N} =-\displaystyle\frac{ \partial \cal{\ln Z} }{ \partial \alpha }$

N =-@DIFF( ln( Z ), alpha )

(ID 3645)

$U =-\displaystyle\frac{\partial\ln{ \cal Z }}{\partial \beta }$

U =-dln( calZ )/ dbeta

(ID 3652)

${\cal Z} =\displaystyle\sum_N\displaystyle\sum_r e^{- \beta E_r - \alpha N }$

Z =@SUM( N * @SUM(exp(- beta * E - alpha * N ), r ))

(ID 3654)

Examples

ID:(473, 0)