Which law governs radiant heat transfer and shows dependence on the fourth power of temperature?

• A. Stefan-Boltzmann Law
• B. Fourier's Law
• C. Newton's Law of Cooling
• D. Planck's Law

Answer: (A)

Radiant heat transfer is described by the Stefan-Boltzmann law, which says that the power radiated per unit area from a body is proportional to the fourth power of its absolute temperature, with the emissivity of the surface adjusting that amount for real materials. In formula terms, the net radiative transfer between bodies is proportional to the difference in T^4 terms, and includes the Stefan-Boltzmann constant and the surface emissivity: q_rad ∝ ε σ (T1^4 − T2^4) for two surfaces at temperatures T1 and T2. The requirement that temperature be in Kelvin reflects the absolute temperature dependence. Planck's Law describes the spectral distribution of the emitted radiation, and when you integrate that spectrum across all wavelengths, you arrive at Stefan-Boltzmann’s result. Fourier's Law governs conduction, and Newton's Law of Cooling is a simple convective-type relation linking heat transfer to a temperature difference, not the fourth-power dependence.