AP EAMCET · PHYSICS · Thermal Properties of Matter
A rectangular metal plate \(8 \mathrm{~cm} \times 4 \mathrm{~cm}\) at \(127^{\circ} \mathrm{C}\) emits \(E \mathrm{Js}^{-1}\). If both length and breadth are halved and the temperature is raised to \(327^{\circ} \mathrm{C}\), the rate of emission is
- A \(\left(\frac{9}{4}\right) E \mathrm{Js}^{-1}\)
- B \(\left(\frac{81}{64}\right) E \mathrm{Js}^{-1}\)
- C \(\left(\frac{27}{8}\right) E \mathrm{Js}^{-1}\)
- D \(\left(\frac{10}{7}\right) E \mathrm{Js}^{-1}\)
Answer & Solution
Correct Answer
(B) \(\left(\frac{81}{64}\right) E \mathrm{Js}^{-1}\)
Step-by-step Solution
Detailed explanation
According to Stefan-Boltzmann's law, rate of emission of radiation from metal surface is given as, \(\begin{aligned} E & =\sigma A T^4 \\ \Rightarrow \quad \frac{E_2}{E_1} & =\left(\frac{A_2}{A_1}\right)\left(\frac{T_2}{T_1}\right)^4 \quad \ldots (i) \end{aligned}\)…
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