Boltzmann Ratio Calculator

Calculate Boltzmann Ratio



Formula

The formula to calculate the Boltzmann Ratio (N2/N1) is:

\[ \frac{N2}{N1} = e^{\left(-\frac{\Delta E}{k_B \cdot T}\right)} \]

Where:

Definitions

Example

Let's say the energy difference is \( 2 \times 10^{-21} \) Joules and the temperature is 300 Kelvin. Using the formula:

\[ \frac{N2}{N1} = e^{\left(-\frac{2 \times 10^{-21}}{1.380649 \times 10^{-23} \cdot 300}\right)} \]

We get:

\[ \frac{N2}{N1} \approx 0.617 \]

So, the Boltzmann Ratio (\( \frac{N2}{N1} \)) is approximately 0.617.

Extended information about "Boltzmann-Ratio-Calculator"

Boltzmann Constant in Calculator

Definition: The Boltzmann constant relates the average kinetic energy of particles in a gas with the temperature of the gas.

Formula: \( k_B = 1.380649 \times 10^{-23} , \text{J/K} \)

Example: \( k_B = 1.380649 \times 10^{-23} \)

Stefan-Boltzmann Equation Calculator

Definition: The Stefan-Boltzmann law describes the power radiated from a black body in terms of its temperature.

Formula: \( P = \sigma A T^4 \)

Example: \( P = 5.67 \times 10^{-8} \times 2 \times (300)^4 \)

Calculation of Boltzmann Constant

Definition: The Boltzmann constant is a fundamental physical constant that relates the average kinetic energy of particles in a gas with the temperature of the gas.

Formula: \( k_B = \frac{R}{N_A} \)

Example: \( k_B = \frac{8.314}{6.022 \times 10^{23}} \)

Stefan-Boltzmann Law Calculator

Definition: The Stefan-Boltzmann law states that the total energy radiated per unit surface area of a black body is directly proportional to the fourth power of the black body's temperature.

Formula: \( E = \sigma T^4 \)

Example: \( E = 5.67 \times 10^{-8} \times (400)^4 \)