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: Understanding the Concept:
By the Stefan-Boltzmann law, the power radiated by a surface is \(P = e\sigma A T^4\), where \(e\) is the emissivity. A perfect black body has \(e = 1\).

Step 2: Black body.
\(R = \sigma A T^4\).

Step 3: Second body.
Same area, \(e = 0.2\) and temperature \(3T\):
\[ P = 0.2\,\sigma A(3T)^4 = 0.2\times 81\,\sigma A T^4 = 16.2\,R \]

Step 4: Check the options.
Option (B) uses \(3^1\) and (D) ignores the temperature. Only 16.2R fits \(0.2\times 3^4\).

Final Answer:
The rate of radiation is \(16.2R\), option (C). \[ \boxed{16.2R} \]