Plain-English Meaning
The hotter something is, the more it radiates — and it scales very steeply with temperature (T to the fourth power!). Double the temperature and you get 2⁴ = 16 times more radiation. σ = 5.67 × 10⁻⁸ W/(m²·K⁴) is the Stefan–Boltzmann constant.
Write the system boundary first. Many thermodynamics mistakes disappear once you know what counts as heat, work, and internal-energy change.
Deeper Explanation
For a perfect blackbody (emissivity ε = 1): P = σAT⁴. For real surfaces: P = εσAT⁴ (0 < ε ≤ 1). Net power exchanged between two surfaces: P_net = εσA(T₁⁴ − T₂⁴). Used to find stellar luminosity: L = 4πR²σT⁴.
Worked Example
Problem: The Sun has radius 6.96×10⁸ m and surface temperature 5778 K. Calculate its luminosity.
- A = 4πR² = 4π × (6.96×10⁸)² = 6.087×10¹⁸ m²
- L = σAT⁴ = 5.67×10⁻⁸ × 6.087×10¹⁸ × (5778)⁴
- (5778)⁴ ≈ 1.114×10¹⁵
- L = 5.67×10⁻⁸ × 6.087×10¹⁸ × 1.114×10¹⁵ ≈ 3.85×10²⁶ W
Result: L ≈ 3.85 × 10²⁶ W (matches the accepted value)
Study Next
Open the full formula deep dive
Take a 10-question quiz on this area
At A Glance
Category: Thermodynamics
Levels covered: High School, College, Masters, PhD
Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.