Stefan's Law Calculator

Stefan-Boltzmann Law:

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

Radiated Power (P):

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1. What is 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 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:

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

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 shows that radiation increases dramatically with temperature, following a T⁴ relationship.

3. Importance of Radiated Power Calculation

Details: This calculation is crucial in astrophysics, thermodynamics, and engineering for determining heat transfer through radiation, designing thermal systems, and studying stellar properties.

4. Using the Calculator

Tips: Enter surface area in square meters and temperature in Kelvin. Both 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, and Kelvin is the SI unit for thermodynamic temperature where 0K represents absolute zero.

Q3: How accurate is this calculation for real objects?
A: Real objects are not perfect black bodies, so the calculated power represents the maximum possible radiation. Real objects emit less radiation, described by their emissivity.

Q4: What are typical applications of this law?
A: Applications include calculating stellar radiation, designing radiators and cooling systems, infrared thermography, and thermal imaging.

Q5: How does surface area affect radiated power?
A: Radiated power is directly proportional to surface area - doubling the surface area doubles the total radiated power at the same temperature.