First slide

Radiation

Question

Two spheres, A & B, are made up of the same material. The radius of A is twice that of B, while the temperature of A is half that of B. What is their ratio of energy emitted per unit time (E_A : E_B)?

Easy

A

1
B

$\frac{1}{2}$
C

$\frac{1}{4}$
D

$\frac{1}{8}$

Solution

Energy emitted per unit time is given by $σ e A T^{4}$ .
e & σ will be the same for both.
A = 4πr²
$\frac{E_{A}}{E_{B}} = \frac{r_{A}^{2}}{r_{B}^{2}} \frac{T_{A}^{4}}{T_{B}^{4}} = \frac{4}{1} \frac{1}{16} = \frac{1}{4}$

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