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Stefan-Boltzmann Law:
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The Stefan-Boltzmann law describes the power radiated from a black body in terms of its temperature. It states that the total energy radiated per unit surface area of a black body is proportional to the fourth power of the black body's absolute temperature.
The calculator uses the Stefan-Boltzmann law:
Where:
Explanation: The law shows that radiation increases rapidly with temperature (to the fourth power), meaning small temperature changes cause large changes in radiated energy.
Details: This calculation is crucial in astrophysics, climate science, thermodynamics, and engineering applications involving heat transfer and thermal radiation.
Tips: Enter surface area in square meters and temperature in Kelvin. Both values must be positive numbers.
Q1: What is a black body in physics?
A: A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.
Q2: How accurate is this for real-world objects?
A: Real objects emit less radiation than a perfect black body. Their emission is described by the equation \( P = \epsilon \sigma A T^4 \), where ε is emissivity (0 ≤ ε ≤ 1).
Q3: Why is temperature raised to the fourth power?
A: This comes from integrating Planck's law over all wavelengths and solid angles, showing that total radiated energy increases extremely rapidly with temperature.
Q4: What are typical applications of this law?
A: Applications include calculating star luminosities, designing radiators and insulation systems, thermal imaging, and climate modeling.
Q5: How was the Stefan-Boltzmann constant determined?
A: It was first determined experimentally by Josef Stefan in 1879 and later derived theoretically by Ludwig Boltzmann in 1884 using thermodynamics.