MHT CET · Physics · Thermal Properties of Matter
A black body at a temperature of \(227^{\circ} \mathrm{C}\) radiates heat energy at the rate \(5 \mathrm{cal} / \mathrm{cm}^{2}-\mathrm{s} .\) At a temperature of \(727^{\circ} \mathrm{C}\), the rate of heat radiated per unit area in \(\mathrm{cal} / \mathrm{cm}^{2}\) will be
- A 80
- B 160
- C 250
- D 500
Answer & Solution
Correct Answer
(A) 80
Step-by-step Solution
Detailed explanation
\(\frac{E_{2}}{E_{1}}=\left(\frac{T_{2}}{T_{1}}\right)^{4}\)
\(
\begin{array}{l}
\frac{E_{2}}{E_{1}}=\left(\frac{273+727}{273+227}\right)^{4} \\
\frac{E_{2}}{5}=\frac{(1000)^{4}}{(500)^{4}}=16 \\
E_{2}=80 \mathrm{cal} / \mathrm{cm}^{2}
\end{array}
\)
\(
\begin{array}{l}
\frac{E_{2}}{E_{1}}=\left(\frac{273+727}{273+227}\right)^{4} \\
\frac{E_{2}}{5}=\frac{(1000)^{4}}{(500)^{4}}=16 \\
E_{2}=80 \mathrm{cal} / \mathrm{cm}^{2}
\end{array}
\)
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