Boltzmann Factor Calculator

Boltzmann Factor Calculator :

Enter the E₁ in electron volts(eV), E₂ in electron volts(eV), and Temperature in celsius(°C), and you get below the calculator.

Boltzmann Factor Calculator

Boltzmann Formula :

Boltzmann formula is the probability at which that this sate occurs P1 / P2  is equal to the exp and multiply the E1 is the energy of the state 1 E1(j) in joules and minutes the E2 is the Energy of the state 2 E2(j) in joules and divided by the Boltzmann constant KB(j/k) in joule per kilo and multiply the temperature T(k) in kelvins. Hence the Boltzmann formula can be written as

P1 / P2 = exp (- (E1(j) – E2(j) ) / (KB(j/k) *T(k) )

Derivation :

Boltzmann Distribution or Gibbs distribution

P=1/Z * exp (-E /( KB *T )

z = normalization constant

E= Energy of state in joules

KB =1.38065 *10 ^(-23 ) J/K is the Boltzmann constant

T= temperature in kelvins

P=probability at which that this sate occurs

Boltzmann factor tells us the relative probability with which two states of Energies E1 and E2 occurs. Dividing the Boltzmann Distribution for these two states we get

P1 / P2 =exp (- (E1 – E2 ) / (KB *T )

It is evident that relative probability depends on the difference of energies. The other factor that plays a vital role in Boltzmann Factor is temperature. The Lower the Temperature is the more probable is the state of lower Energy

Boltzmann factor Example: 1

Calculate the probability value? Energy of state 9 joules and 2nd energy state 9 joules and temperature 5K .

Solution:

E1=9 joules

E2=9 joules

T=5k

By using formula

P1 / P2 = exp (- (E1 – E2 ) / (KB *T )

P1 / P2 = exp (9-9 ) / (1.38065 *10-23  * 5)

Boltzmann factor =1

Boltzmann Factor Example: 2

Calculate the probability value? Energy of state  35 joules and 2nd energy state 35  joules and temperature 12K .

Answer:

E1=35 joules

E2=35 joules

T=12 k

By using formula

P1 / P2 = exp (- (E1 – E2 ) / (KB *T )

P1 / P2 = exp (35 – 35 ) / (1.38065 *10-23  * 12)

Boltzmann factor =1

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