Black body radiation

Black body radiation refers to the type of electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by a black body (an opaque and non-reflective body) held at constant, uniform temperature. The radiation has a specific spectrum and intensity that depends only on the temperature of the body.

Overview

A black body in thermodynamics is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. A white body is one with a "rough surface [that] reflects all incident rays completely and uniformly in all directions."

A black body in thermal equilibrium (that is, at a constant temperature) emits electromagnetic radiation called black body radiation. The radiation emitted by a black body is continuous, it does not depend on the material of the body, and has a characteristic frequency distribution that depends on the temperature. The radiation is isotropic, meaning that the body emits radiation uniformly in all directions.

Laws of Black Body Radiation

The study of black body radiation led to the development of the quantum mechanics field in the 20th century. Two main laws describe the behavior of black body radiation:

Planck's Law

Planck's Law describes the spectrum of black body radiation, which depends only on the body's temperature. Max Planck proposed this law in 1900, which was a significant milestone in the development of quantum theory. The law indicates that the energy emitted at different frequencies by a black body does not follow the classical Rayleigh-Jeans law, which predicted an ultraviolet catastrophe at high frequencies. Instead, Planck's law accurately predicts the intensity of the radiation, which reaches a maximum at a frequency that increases with the temperature of the body.

Stefan-Boltzmann Law

The Stefan-Boltzmann Law states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time (also known as the black body's radiant exitance or emissive power) is directly proportional to the fourth power of the black body's thermodynamic temperature T. The constant of proportionality is known as the Stefan-Boltzmann constant, \(\sigma\), which is a fundamental physical constant. This law highlights the relationship between the temperature of a black body and its total emission.

Applications

Black body radiation has applications in various fields, including:

• Astronomy: In studying the temperature and properties of stars, including our sun, which can be approximated as black bodies.
• Climate science: In understanding the Earth's absorption and emission of solar radiation and its impact on climate.
• Thermography: In using infrared cameras to detect radiation in the environment to measure temperature.

See Also

• Electromagnetic spectrum
• Quantum mechanics
• Thermodynamics
• Wein's Displacement Law