1. What is the Stefan-Boltzmann Constant?

The Stefan-Boltzmann constant (σ) relates the total energy radiated per unit surface area of a black body to the fourth power of its thermodynamic temperature. It appears in the Stefan-Boltzmann law of black-body radiation.

2. How Does the Calculator Work?

The calculator uses the fundamental constants to derive σ:

Where:

• \( k \) — Boltzmann constant (1.38 × 10^-23 J/K)
• \( h \) — Planck constant (6.626 × 10^-34 J·s)
• \( c \) — Speed of light (3 × 10⁸ m/s)
• \( \pi \) — Mathematical constant pi (~3.14159)

Explanation: The constant is derived from fundamental physical constants and quantum theory principles.

3. Importance of the Constant

Details: The Stefan-Boltzmann constant is crucial in thermodynamics, astrophysics, and climate science for calculating radiation from stars, planets, and other black-body radiators.

4. Using the Calculator

Tips: Enter the fundamental constants in their standard scientific notation forms. Default values are provided for convenience.

5. Frequently Asked Questions (FAQ)

Q1: What is the accepted value of σ?
A: The accepted value is approximately 5.670374419 × 10^-8 W/m²·K⁴.

Q2: Why is this constant important?
A: It's fundamental for calculating black-body radiation and appears in many areas of physics and engineering.

Q3: Can I use different units?
A: The calculator uses standard SI units. For other unit systems, conversion would be needed.

Q4: How precise is this calculation?
A: The precision depends on the input values of the fundamental constants used.

Q5: What's the relationship with Wien's law?
A: Both relate to black-body radiation, but Wien's law describes the peak wavelength while Stefan-Boltzmann describes total power.