Radiation fundamental — name the law: Q = σ A T^4 Identify the classical radiation relation that states total emissive power of a black surface varies with the fourth power of absolute temperature.

Introduction / Context:
Thermal radiation differs from conduction and convection because it requires no medium. A core result links total radiant emission from an ideal black surface to temperature.

Given Data / Assumptions:

• Q = σ * A * T^4 where σ is the Stefan–Boltzmann constant, A is area, and T is absolute temperature.
• Relation applies to an ideal blackbody; real surfaces use Q = ε * σ * A * T^4 with emissivity ε.

Concept / Approach:
The statement describes the Stefan–Boltzmann law, a cornerstone of radiation heat transfer. It shows a strong temperature dependence: small increases in T cause large increases in radiative emission.

Step-by-Step Solution:

Verification / Alternative check:
Fourier’s law uses q = −k * dT/dx (linear gradient); Newton’s law uses q = h * A * ΔT (linear in ΔT). Neither has a T^4 term.

Why Other Options Are Wrong:

Fourier: conduction law, no T^4.Newton–Rikhmann: convection correlation, linear in temperature difference.Joseph–Stefan: not a standard heat-transfer law.Planck’s law: spectral distribution, not total emissive power.

Common Pitfalls:
Confusing total emissive power (Stefan–Boltzmann) with wavelength-dependent emission (Planck). For real surfaces, include emissivity.

Final Answer:

Stefan–Boltzmann equation