If the temperature of a black body doubles, how many times will its emissive power increase?

Question

Question

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RRB JE ME 22 Apr 2025 Shift 2 CBT 2 Official Paper

Answer 1

Explanation:

Black Body:

A black body is an idealized physical object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. A black body also emits radiation in a characteristic spectrum that depends only on its temperature, as described by Planck's Law.

Emissive Power:

Emissive power of a black body refers to the total energy radiated per unit surface area per unit time. This is given by the Stefan-Boltzmann Law, which states:

E = σT⁴

Where:

Calculation:

If temperature doubles: T' = 2T

\( E' = \sigma (2T)^4 = 16 \cdot \sigma T^4 = 16E \)