According to the Stefan–Boltzmann (Stefan’s) law of thermal radiation, the total emissive power of an ideal black body is proportional to which function of its absolute temperature?

Introduction / Context:
Radiative heat transfer from ideal black bodies follows a fundamental law that connects temperature to radiant energy emission. Recognizing the T^4 dependence is essential for high-temperature furnace design, spacecraft thermal control, and heat loss estimates in power equipment.

Given Data / Assumptions:

• Black body is an ideal emitter with emissivity ε = 1.
• Total emissive power E_b sums radiation over all wavelengths.

Concept / Approach:
Stefan–Boltzmann law states E_b = σ * T^4, where σ is the Stefan–Boltzmann constant. For real surfaces, E = ε * σ * T^4 with 0 < ε ≤ 1. The key takeaway is the fourth-power dependence on absolute temperature (kelvin). Small temperature increases can therefore create large changes in radiative heat transfer.

Step-by-Step Solution:

Verification / Alternative check:
Dimensional and empirical verifications are standard in heat transfer texts and laboratory black-body furnaces; the T^4 trend is well established.

Why Other Options Are Wrong:

• T^1, T^2, ln T, or 1/T: Do not represent total emissive power for a black body.

Common Pitfalls:
Confusing monochromatic laws (Planck’s law, Wien’s displacement) with total emissive power; forgetting to use absolute temperature in kelvin.

Final Answer:
Fourth power of temperature (T^4)