Planck's Function in Physics

Planck’s Function

• Planck's function defines the relationship between temperature (T) and wavelength (λ) for radiance (Bλ) measured in Wm²Sr⁻¹μm⁻¹.
• Boltzmann’s constant (kB) is 1.381 x 10⁻²³ JK⁻¹, used in the calculation of thermal energy.
• The speed of light (c) is 2.998 x 10⁸ m/s, essential for understanding electromagnetic radiation.
• Planck’s constant (h) equals 6.626 x 10⁻³⁴ Js, fundamental in quantum mechanics.
• Absolute temperature (T) is measured in Kelvin (K), the standard unit for thermodynamic temperature.
• Wavelength (λ) is expressed in micrometers (μm).

Wien’s Displacement Law

• T represents absolute temperature, indicating that peak wavelength emission is inversely proportional to temperature.
• Wien's displacement constant (b) is approximately 2.897771955 x 10⁻³ m⋅K, used to find peak emission wavelengths.
• Cooler objects, like Earth, emit longer wavelengths compared to hotter objects, like the Sun, which emit at shorter wavelengths.

Stefan-Boltzmann Law

• The radiant energy (E) emitted per unit area in one second is given by E = σT⁴, with σ as the Stefan-Boltzmann constant.
• The emission per unit area of a black body is directly proportional to the fourth power of absolute temperature (T).

Emission

• Emission is the process of converting internal energy into radiant energy, occurring at all temperatures above absolute zero (0 K).
• Human bodies lose heat energy via radiation but rarely notice due to heat balance with surroundings.
• Examples of emission include heat felt from a burning stove and visible radiation from glowing embers.

Emissivity

• Emissivity measures the emitted radiation of a surface compared to that of a black body.
• Monochromatic emissivity refers to emission at a single wavelength, while graybody emissivity pertains to emission across a spectrum of wavelengths.

Blackbody Characteristics

• A blackbody is an ideal emitter with maximum radiation at all wavelengths, fully absorbing all incident radiation.
• Blackbody radiation is determined solely by the emitter's temperature, showcasing maximum possible radiant energy at given temperatures.
• The radiation emitted by a blackbody is isotropic, meaning it is uniform in all directions.

Planck’s Radiation Law

• Describes the spectral density of radiation emitted by a black body in thermal equilibrium at temperature T.
• A black body emits radiation across all wavelengths, but there exists a maximum amount for any specific wavelength at a defined temperature.