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Q.

A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P) by the metal. The sensor has a scale that displays log2PP0 where P0 is a constant. When the metal surface is at a temperature of 487 0C , the sensor shows a value 1. Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to 2767 0C ?

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answer is 9.

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Detailed Solution

Tin =273+487=760KTfin =2767+273=3040K=4Tin Since, P ∝ T4⇒Pfinal =44Pin Initial reading =log2⁡Pin P0=1⇒Pin P0=2 Final reading =log2⁡44Pin P0=log2⁡29=9

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A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P) by the metal. The sensor has a scale that displays log2PP0 where P0 is a constant. When the metal surface is at a temperature of 487 0C , the sensor shows a value 1. Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to 2767 0C ?