Determine the temperature at which the radiant luminosity of a blackbody is Rt = 459 W / m2.

We need to determine the temperature at which the radiant luminosity of an absolutely black body is Rt = 459 W / m ^ 2.

We start the solution with a short note given.

Given:

Rt = 459 W / m2

T – ? (temperature).

Solution:

To solve, we apply the Stefan-Boltzmann law, which we write in the form of a formula as follows:

R * t = σ * T ^ 4.

Where

σ = (2n ^ 5 * k ^ 4) / (15c ^ 2 h ^ 3).

σ ≈ 5.67 * 10 ^ (- 8) W / (m ^ 2 * k ^ 4), where

k is Boltzmann’s constant.

From here

T = ⁴√ (Rt / σ).

T = ⁴√ (459 / (5.67 * 10 ^ (- 8))) ≈ 300 K.