Question

Rate of radiation by a black body is 'R' at temperature 'T'. Another body has same area but emissivity is 0.2 and temperature 3T. Its rate of radiation is

• A. \(R\)
• B. \(2R\)
• C. \(16.2R\)
• D. \(0.2R\)

Hint:

Radiated power varies as emissivity times the fourth power of temperature, with the black body having emissivity 1.

Answer 1

The Correct Option is C

Step 1: Take the ratio.
$\dfrac{P}{R} = \dfrac{e_2}{e_1}\left(\dfrac{T_2}{T_1}\right)^4$ for equal areas.

Step 2: Substitute.
$e_2/e_1 = 0.2/1$ and $T_2/T_1 = 3$, so the ratio is $0.2 \times 81$.

Step 3: Compute.
$0.2 \times 81 = 16.2$.

Final Answer:
Option (C). \[ \boxed{16.2R} \]