MHT CET · Physics · Thermal Properties of Matter
Three black discs ' \(\mathrm{x}^{\prime}\), \(^{\prime} \mathrm{y}^{\prime},{ }^{\prime} \mathrm{z}^{\prime}\) have radii \(1 \mathrm{~m}, 2 \mathrm{~m}\) and \(3 \mathrm{~m}\) respectively. The wavelengths corresponding to maximum intensity are 200,300 and \(400 \mathrm{~nm}\) respectively. The relation between emissive powers 'Ex', 'Ey' and 'Ez' is
- A \(\mathrm{Ex}>\mathrm{Ey} < \mathrm{Ez}\)
- B \(\mathrm{Ex} < \mathrm{Ey} < \mathrm{Ez}\)
- C \(\mathrm{Ex}=\mathrm{Ey}=\mathrm{Ez}\)
- D \(\mathrm{Ex}>\mathrm{Ey}>\mathrm{Ez}\)
Answer & Solution
Correct Answer
(D) \(\mathrm{Ex}>\mathrm{Ey}>\mathrm{Ez}\)
Step-by-step Solution
Detailed explanation
\(\lambda_{\mathrm{m}} \mathrm{T}=\mathrm{k}\)
\(\mathrm{E}=\frac{\sigma \mathrm{AT}^{4}}{\mathrm{~A}} \Rightarrow \mathrm{E} \propto \mathrm{T}^{4} \quad \therefore \mathrm{E} \propto \frac{\mathrm{A}}{\lambda^{4}}\)
\(\mathrm{E}_{\mathrm{x}}: \mathrm{E}_{\mathrm{y}}: \mathrm{E}_{\mathrm{z}}=\frac{1}{\lambda_{\mathrm{x}}^{4}}: \frac{1}{\lambda_{\mathrm{y}}^{4}}: \frac{1}{\lambda_{\mathrm{z}}^{4}}=\frac{1}{(200)^{4}}: \frac{1}{(300)^{4}}: \frac{1}{(400)^{4}}\)
\(\mathrm{E}_{\mathrm{x}}>\mathrm{E}_{\mathrm{y}}>\mathrm{E}_{\mathrm{z}}\)
\(\mathrm{E}=\frac{\sigma \mathrm{AT}^{4}}{\mathrm{~A}} \Rightarrow \mathrm{E} \propto \mathrm{T}^{4} \quad \therefore \mathrm{E} \propto \frac{\mathrm{A}}{\lambda^{4}}\)
\(\mathrm{E}_{\mathrm{x}}: \mathrm{E}_{\mathrm{y}}: \mathrm{E}_{\mathrm{z}}=\frac{1}{\lambda_{\mathrm{x}}^{4}}: \frac{1}{\lambda_{\mathrm{y}}^{4}}: \frac{1}{\lambda_{\mathrm{z}}^{4}}=\frac{1}{(200)^{4}}: \frac{1}{(300)^{4}}: \frac{1}{(400)^{4}}\)
\(\mathrm{E}_{\mathrm{x}}>\mathrm{E}_{\mathrm{y}}>\mathrm{E}_{\mathrm{z}}\)
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