The spectrum of a black body at two temperatures $27℃$ and $327℃$ is shown in the figure. Let $A_{1}$ and $A_{2}$ be the areas under the two curves respectively. The value of $\frac{A_{2}}{A_{1}}$ is [image:11_image29.emf]

Question

Dr. Abubacker · Accepted Answer

(d) Area under given curve represents emissive power and emissive power $\propto T^{4} \Rightarrow A \propto T^{4}$
$\Rightarrow \frac{A_{2}}{A_{1}} = \frac{T_{2}^{4}}{T_{1}^{4}} = \frac{(273 + 327)^{4}}{(273 + 27)^{4}} = \left( \frac{600}{300} \right)^{4} = \frac{16}{1}$

Q. The spectrum of a black body at two temperatures $27℃$ and $327℃$ is shown in the figure. Let $A_{1}$ and $A_{2}$ be the areas under the two curves respectively. The value of $\frac{A_{2}}{A_{1}}$ is

Explanation

Reviewed by Dr. Abubacker

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