The temperature of a spherical black body is inversely proportional to its radius. If its radius is doubled,…

The temperature of a spherical black body is inversely proportional to its radius. If its radius is doubled, then the power radiating from it will be
  1. doubled
  2. $\frac{1}{4}$ times of initial value
  3. halved
  4. four times of initial value

Solution


From Eqs. (i), (ii) and (iii), we have, $ P=\sigma 4 \pi R^2 \cdot\left(\frac{k^4}{R^4}\right) \text { or } P \propto \frac{1}{R^2} $ So, when radius is doubled, radiating power of sphere becomes one fourth

Asked in: AP EAMCET 2018 (24 Apr Shift 1)

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