Boltzmann Ratio Calculator

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:

\( \frac{N2}{N1} \) is the Boltzmann ratio.
\( \Delta E \) is the energy difference in joules.
\( k_B \) is the Boltzmann constant (approximately \( 1.380649 \times 10^{-23} \) J/K).
\( T \) is the temperature in Kelvin.

Definitions

Boltzmann Ratio: The relative population of particles in different energy states at thermal equilibrium.
Energy Difference (ΔE): The difference in energy between two states, measured in joules.
Boltzmann Constant (kB): A physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas, approximately \( 1.380649 \times 10^{-23} \) J/K.
Temperature (T): The measure of the thermal energy of a system, measured in Kelvin.

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

\( k_B \): Boltzmann constant

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

\( k_B \): Boltzmann constant

Stefan-Boltzmann Equation Calculator

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

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

\( P \): Power radiated
\( \sigma \): Stefan-Boltzmann constant
\( A \): Surface area
\( T \): Temperature in Kelvin

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

\( P \): Power radiated
\( \sigma \): (5.67 \times 10^{-8} , \text{W/m}^2\text{K}^4)
\( A \): 2 m²
\( T \): 300 K

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

\( k_B \): Boltzmann constant
\( R \): Universal gas constant
\( N_A \): Avogadro's number

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

\( k_B \): Boltzmann constant
\( R \): 8.314 J/mol·K
\( N_A \): (6.022 \times 10^{23} , \text{mol}^{-1})

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

\( E \): Energy radiated per unit area
\( \sigma \): Stefan-Boltzmann constant
\( T \): Temperature in Kelvin

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

\( E \): Energy radiated per unit area
\( \sigma \): (5.67 \times 10^{-8} , \text{W/m}^2\text{K}^4)
\( T \): 400 K