Question

Rate of radiation by a black body is $R$ at temperature $T$. Another body has the same area but emissivity is $0.2$ and temperature is $3T$. Its rate of radiation is

• A. $(8.1)R$
• B. $(16.2)R$
• C. $(24.3)R$
• D. $(32.4)R$

Hint:

Radiated power varies as the fourth power of absolute temperature.

Answer 1

The Correct Option is B

Step 1: Apply Stefan–Boltzmann law.
The power radiated is given by: \[ P = e \sigma A T^4 \] Step 2: Radiation from black body.
For a black body, emissivity $e = 1$, hence: \[ R = \sigma A T^4 \] Step 3: Radiation from second body.
\[ P' = 0.2 \times \sigma A (3T)^4 \] Step 4: Simplification.
\[ P' = 0.2 \times 81 \times \sigma A T^4 = 16.2 \sigma A T^4 \] Step 5: Final comparison.
\[ P' = 16.2R \]