Stefan Boltzmann Law Calculator

Stefan Boltzmann Law:

\[ P = \sigma A T^4 \]

Radiated Power (P):

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1. What is the Stefan Boltzmann Law?

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 across all wavelengths per unit time is directly proportional to the fourth power of the black body's thermodynamic temperature.

2. How Does the Calculator Work?

The calculator uses the Stefan Boltzmann Law:

\[ P = \sigma A T^4 \]

Where:

\( P \) — Radiated power (W)
\( \sigma \) — Stefan Boltzmann constant (5.67 × 10⁻⁸ W/m²K⁴)
\( A \) — Surface area (m²)
\( T \) — Temperature (K)

Explanation: The law quantifies the relationship between temperature and radiated energy, showing that radiation increases dramatically with temperature (T⁴ dependence).

3. Importance of Radiated Power Calculation

Details: This calculation is crucial in thermodynamics, astrophysics, and engineering applications including heat transfer analysis, star luminosity estimation, and thermal radiation studies.

4. Using the Calculator

Tips: Enter surface area in square meters and temperature in Kelvin. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a black body?
A: A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.

Q2: Why is temperature in Kelvin?
A: The Stefan Boltzmann Law requires absolute temperature because it's derived from thermodynamic principles where zero temperature corresponds to zero radiation.

Q3: How accurate is this for real objects?
A: Real objects are not perfect black bodies. Their actual radiation is given by P = εσAT⁴, where ε is the emissivity (0 ≤ ε ≤ 1).

Q4: What are typical applications?
A: This law is used in calculating star temperatures, designing thermal systems, infrared thermography, and understanding climate science.

Q5: Why the fourth power relationship?
A: The T⁴ dependence comes from the integration of Planck's law over all wavelengths and solid angles, reflecting how radiation intensity increases dramatically with temperature.