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MHT CET · Physics · Thermal Properties of Matter

A black sphere has radius R whose rate of radiation is E at temperature T. If radius is made R/2 and temperature 3T, the rate of radiation will be

  1. A \(\frac{3 \mathrm{E}}{2}\)
  2. B \(\frac{27 E}{8}\)
  3. C \(\frac{81 \mathrm{E}}{4}\)
  4. D \(\frac{9 E}{4}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{81 \mathrm{E}}{4}\)

Step-by-step Solution

Detailed explanation

\(E \propto R^2 T^4\) \(\frac{E'}{E} = \frac{(R/2)^2 (3T)^4}{R^2 T^4} = \frac{(R^2/4) (81T^4)}{R^2 T^4} = \frac{81}{4}\)