First slide

Heat transfer-Radiation

Question

Three discs A, B and C having radii 2m, 4m, and 6m respectively are coated with carbon black on their other surfaces. The wavelengths corresponding to maximum intensity are 300 run, 400 nm and 500 nm, respectively. The power radiated by them are Q_a, Q_b, and Q_c, respectively,

Moderate

A

$Q_{a} is maximum$
B

$Q_{b} is maximum$
C

$Q_{c} is maximum$
D

$Q_{a} = Q_{b} = Q_{c}$

Solution

$Radiated power P = {AeσT}^{4} \Rightarrow P \propto {AT}^{4}$
$From Wein's law, λ_{m} T = constant \Rightarrow T \propto \frac{1}{λ_{m}}$
$\begin{array}{l} ∴ P \propto \frac{A}{{(λ_{m})}^{4}} \propto \frac{r^{2}}{{(λ_{m})}^{4}} \\ \Rightarrow Q_{A} : Q_{B} : Q_{C} = \frac{2^{2}}{(300)^{4}} : \frac{4^{2}}{(400)^{4}} : \frac{6^{2}}{(500)^{4}} \end{array}$
$∴ Q_{B} will be maximum.$

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