Stefan-Boltzmann Law Calculator

Select Material:

Emissivity (\( \epsilon \), 0–1):

Surface Area (\( A \)):

Temperature (\( T \)):

1. What is the Stefan-Boltzmann Law Calculator?

Definition: This calculator uses the Stefan-Boltzmann law to compute the power of thermal radiation (\( P \)) emitted by a body based on its emissivity (\( \epsilon \)), surface area (\( A \)), and temperature (\( T \)).

Purpose: It is used in thermodynamics and astrophysics to determine the rate at which an object emits thermal radiation, which is essential for understanding heat transfer and the behavior of celestial bodies like stars.

2. How Does the Calculator Work?

The calculator uses the following equation:

\( P = \sigma \times \epsilon \times A \times T^4 \)

Where:

\( P \): Power of thermal radiation (W, kW, MW);
\( \sigma \): Stefan-Boltzmann constant (\( 5.670367 \times 10^{-8} \, \text{W·m}^{-2}\text{·K}^{-4} \));
\( \epsilon \): Emissivity (0–1);
\( A \): Surface area (m², cm², mm², km²);
\( T \): Temperature (K, °C, °F, converted to K).

Steps:

Select a material to use its predefined emissivity, or choose "Custom" to enter your own value.
Enter the surface area (\( A \)) with its unit.
Enter the temperature (\( T \)) with its unit.
Convert the surface area to \( \text{m}^2 \) and temperature to Kelvin.
Calculate the power: \( P = \sigma \times \epsilon \times A \times T^4 \).
Convert the power to the selected output unit and display, formatted in scientific notation if the absolute value is less than 0.001, otherwise with 4 decimal places.

3. Importance of Stefan-Boltzmann Law Calculation

Calculating the power of thermal radiation is crucial for:

Thermodynamics: Understanding heat transfer via radiation in engineering systems.
Astrophysics: Estimating the energy output of stars and other celestial bodies.
Material Science: Designing materials with specific thermal properties by considering their emissivity.

4. Using the Calculator

Example 1: Calculate the thermal radiation power for a black body (\( \epsilon = 1 \)) with a surface area of 1 m² at 300 K:

Material: Black Body (\( \epsilon = 1 \));
Surface Area: \( A = 1 \, \text{m}^2 \);
Temperature: \( T = 300 \, \text{K} \);
Power: \( P = 5.670367 \times 10^{-8} \times 1 \times 1 \times (300)^4 \approx 459.27 \, \text{W} \);
Result: \( P = 459.2700 \, \text{W} \).

Example 2 (Custom Material): Calculate the thermal radiation power for a concrete surface (\( \epsilon = 0.91 \)) with a surface area of 500 cm² at 25°C:

Material: Concrete (\( \epsilon = 0.91 \));
Surface Area: \( A = 500 \, \text{cm}^2 = 0.05 \, \text{m}^2 \);
Temperature: \( T = 25 \, \text{°C} = 298.15 \, \text{K} \);
Power: \( P = 5.670367 \times 10^{-8} \times 0.91 \times 0.05 \times (298.15)^4 \approx 20.37 \, \text{W} \);
Result: \( P = 20.3700 \, \text{W} \).

5. Frequently Asked Questions (FAQ)

Q: What does the Stefan-Boltzmann law tell us?
A: The Stefan-Boltzmann law quantifies the power radiated by a body due to its temperature, showing that the radiated power is proportional to the fourth power of the temperature and depends on the body's emissivity and surface area.

Q: Why does emissivity matter?
A: Emissivity (\( \epsilon \)) determines how efficiently a body emits thermal radiation compared to a perfect black body (\( \epsilon = 1 \)). Lower emissivity means less radiation is emitted, as seen with reflective surfaces like aluminum foil.

Q: Can this calculator be used for non-ideal black bodies?
A: Yes, the calculator accounts for real materials by using their emissivity values, which can be selected from a predefined list or entered manually.