What infrared law shows the radiated power over the whole spectrum for a given temperature?

Planck's Law provides the framework for understanding how radiated power is distributed across the electromagnetic spectrum for a given temperature of a black body. It describes the spectral density of radiation emitted by a black body as a function of wavelength at a specific temperature. According to Planck's Law, the intensity and distribution of the emitted radiation vary with temperature, producing a characteristic spectrum that peaks at a particular wavelength.

This law is fundamental in thermal radiation and is vital for understanding how infrared radiation behaves at different temperatures, making it a key concept in electronic warfare applications, such as sensing and countermeasure systems that operate in the infrared spectrum.

In contrast, Wein's Displacement Law pertains to the wavelength at which the peak emission occurs for a black body at a given temperature; Kirchhoff's Law of Radiation deals with the relationship between absorption and emission, and Stefan-Boltzmann relates to total energy emission per unit surface area of a black body across all wavelengths, rather than detailing the spectral distribution. Thus, Planck's Law is the correct answer as it directly addresses the radiated power across the entire spectrum for a specific temperature.