TS EAMCET · Physics · Thermal Properties of Matter
A black body radiates energy at the rate of \(E\) watt \(/ \mathrm{m}^2\) at a high temperature \(T \mathrm{~K}\). When the temperature is reduced to \(\left(\frac{T}{2}\right) \mathrm{K}\), the radiant energy is
- A \(\frac{E}{2}\)
- B \(2 E\)
- C \(\frac{E}{4}\)
- D \(\frac{E}{16}\)
Answer & Solution
Correct Answer
(D) \(\frac{E}{16}\)
Step-by-step Solution
Detailed explanation
According to Stefan's law, \(\begin{array}{rlrl} & E \propto T^4 \\ \text { or } & \frac{E_2}{E_1} & =\left(\frac{T_2}{T_1}\right)^4 \\ \text { or } & \frac{E_2}{E} & =\left(\frac{T / 2}{T}\right)^4=\left(\frac{1}{2}\right)^4 \\ \text { or } & E_2 & =\frac{E}{16}\end{array}\)
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