First slide

Radiation

Question

Two objects A and B have same shape and area. The Emissivity of A is 0.2 and that of B is 0.8. Each radiates same power. The ratio of their absolute temperatures is

Easy

A

2 : 1
B

1 : 4
C

1 : √2
D

√2 : 1

Solution

From the surface of a hot body, power radiated is P = eσAT⁴
e_A = 0.2, e_B = 0.8,
$\large e_A.A.\sigma .T^4_A=e_B .A.\sigma .T^4_B$
$\large \frac {e_B}{e_A}= \left ( \frac {T_A}{T_B} \right )^4\Rightarrow \frac {0.8}{0.2}=\left ( \frac {T_A}{T_B} \right )^4$
$\large T_A:T_B=\sqrt 2:1$

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