Stefan-Boltzmann Law of Radiation
The Stefan-Boltzmann law states that the total power radiated per unit surface area of a black body is directly proportional to the fourth power of its absolute temperature. Mathematically:
P = σ A T⁴
Where:
- P: Total power radiated (W),
- σ: Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²·K⁴),
- A: Surface area of the radiating body (m²),
- T: Absolute temperature of the body (K).
For Non-Black Bodies:
For real objects that are not perfect black bodies, the Stefan-Boltzmann law is modified by introducing the emissivity factor (e), which ranges from 0 to 1:
P = e σ A T⁴
Where:
- e: Emissivity of the surface, with e = 1 for a perfect black body and e < 1 for real bodies.
Key Points:
- The power radiated depends heavily on the temperature, as it varies with the fourth power of T.
- Black bodies are idealized objects that absorb and emit radiation perfectly.
- Real objects emit less radiation than a black body of the same temperature, proportional to their emissivity.
Applications of the Stefan-Boltzmann Law:
- Astrophysics: Used to calculate the temperature and luminosity of stars based on their radiation.
- Thermal Imaging: Stefan-Boltzmann law is used to estimate the temperature of objects from their radiated energy.
- Climate Studies: The law helps in modeling Earth’s energy balance and understanding global warming.
- Industrial Applications: Used to design furnaces, radiators, and cooling systems.
Real-Life Examples:
- The Sun radiates energy proportional to its surface temperature, enabling life on Earth.
- Cooling of hot metal after forging occurs due to radiation governed by this law.
- A heated filament in a light bulb emits radiation, which can be analyzed using the Stefan-Boltzmann law.
Graphical Representation:
The graph of P (radiated power) vs. T⁴ (temperature raised to the fourth power) is a straight line, indicating a direct proportionality.
Observations:
- Radiated power increases rapidly with temperature due to the T⁴ dependence.
- Black bodies emit maximum radiation at a given temperature.
- Real objects with lower emissivity radiate less power compared to black bodies.
- Stefan-Boltzmann law applies to all objects emitting thermal radiation, provided emissivity is considered.
The Stefan-Boltzmann law is fundamental in understanding radiation processes, energy transfer, and the thermal behavior of objects in a variety of scientific and engineering applications.
