This tool calculates the radiant heat energy emitted by a black body based on its temperature.
How to Use the Stefan-Boltzmann Law Calculator
The Stefan-Boltzmann Law calculator helps you calculate the radiant heat energy emitted by a black body in thermal equilibrium. To use this calculator:
- Enter the temperature of the black body in Kelvin.
- Enter the emissivity of the material (a value between 0 and 1, where 1 represents a perfect black body).
- Enter the surface area of the black body in square meters.
- Click “Calculate” to see the result in Watts per square meter (W/m²).
Explanation of Stefan-Boltzmann Law
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 absolute temperature (in Kelvin). The formula is given by:
E = σ * ε * T⁴ * A
where:
- E is the total energy radiated per unit surface area (W/m²).
- σ (Stefan-Boltzmann constant) = 5.67 × 10⁻⁸ W/m²K⁴.
- ε is the emissivity of the material.
- T is the absolute temperature in Kelvin (K).
- A is the surface area in square meters (m²).
Limitations
While using this calculator, keep in mind:
- The accuracy of the results depends on the accurate input values of temperature, emissivity, and surface area.
- This calculator assumes that the body is in thermal equilibrium, and that other forms of heat transfer (conduction and convection) are negligible.
- The emissivity value should be between 0 and 1 for realistic results.
Use Cases for This Calculator
Calculate Total Radiant Energy Emitted
Enter the temperature of the object to find out the total radiant energy emitted using Stefan-Boltzmann Law. This calculation helps in determining the amount of energy emitted by an object based on its temperature.
Calculate Temperature of an Object
Specify the total radiant energy emitted by an object to calculate its temperature using Stefan-Boltzmann Law. This feature can be useful in determining the temperature of an object based on the energy it radiates.
Calculate Power Radiated
Input the temperature and surface area of the object to find out the power radiated using Stefan-Boltzmann Law. This computation can help in understanding the rate at which energy is emitted by an object.
Calculate Surface Area Required for Specific Power
Provide the power output and temperature to determine the surface area required for specific power output based on Stefan-Boltzmann Law. This calculation can assist in designing systems to meet specific power requirements.
Calculate Temperature Increase Due to Energy Absorption
Enter the energy absorbed by an object to calculate the increase in temperature using Stefan-Boltzmann Law. This calculation can provide insights into the temperature rise resulting from absorbed energy.
Calculate Minimum Temperature to Radiate Specific Power
Specify the power output required and surface area to determine the minimum temperature needed to radiate that power based on Stefan-Boltzmann Law. This feature can help in setting temperature targets for radiative power emission.
Calculate Radiative Heat Transfer Between Two Objects
Input the temperatures and surface areas of two objects to calculate the radiative heat transfer between them using Stefan-Boltzmann Law. This computation can aid in analyzing heat exchange between objects through radiation.
Calculate Power Density at a Distance
Provide the power output and distance from the object to calculate power density using Stefan-Boltzmann Law. This feature helps in determining the power distribution at various distances from the radiating object.
Calculate Surface Temperature of an Absorbing Object
Input the energy absorbed and surface area of the object to calculate its surface temperature based on Stefan-Boltzmann Law. This calculation can help in understanding the temperature of an object that absorbs a certain amount of energy.
Calculate Energy Required to Reach a Specific Temperature
Specify the initial and desired temperatures of an object to calculate the energy required to reach the desired temperature using Stefan-Boltzmann Law. This calculation can assist in understanding the energy needed for thermal conditioning of objects.