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According to Stefan's law for black body radiation, the temperature of a spherical body can be expressed as a function of heat radiated, surface area, and Stefan-Boltzmann constant. Which of the following represents the correct formula for temperature?

1. T = [Q / (σ(4πR^2))]^(1/4)
2. T = [Q / (σ(4πR^2))]^(1/2)
3. T = [Q / (σ(4πR^2))]^(1/3)
4. T = [Q / (σ(4πR^2))]^(1/5)

Correct answer: T = [Q / (σ(4πR^2))]^(1/4)

Solution

Stefan's law states that the power radiated by a black body is proportional to the fourth power of its temperature. Rearranging the formula Q = σeAT^4 for T, we get T = [Q/(σA)]^(1/4). Substituting A = 4πR^2, the correct expression is T = [Q/(σ(4πR^2))]^(1/4).

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