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 $$2767$$ $$0C$$ ?

Question

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 $$2767$$ $$0C$$ ?

Infinity Learn · Accepted Answer

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

Heat transfer-Radiation

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Heat transfer-Radiation

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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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