Q113 / 200 · NEET 2009 (Screening) · Physics

A black body at $227^{\circ} \mathrm{C}$ radiates heat at the rate of $7 \mathrm{cal} \mathrm{cm}^{-2} \mathrm{~s}^{-1}$. At a temperature of $727^{\circ} \mathrm{C}$, the rate of heat radiated in the same units will be

  • A
    60
  • B
    50
  • Correct answer
    C
    112
  • D
    80

Solution

Key Idea Apply Stefan's law of radiation. $$ \begin{aligned} \mathrm{E} & =\sigma \mathrm{T}^4 \\ \frac{\mathrm{E}_1}{\mathrm{E}_2} & =\left[\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right]^4 \\ \Rightarrow \quad \mathrm{E}_2 & =7\left[\frac{273+727}{273+227}\right]^4 \\ & =\left(\frac{1000}{500}\right)^4 \times 7 \\ & =112 \mathrm{cal}-\mathrm{cm}^{-2} \mathrm{~s}^{-1} \end{aligned} $$

Hence, the correct answer is option: 'C'.

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