A metal is heated in a furnace where a sensor is kept above the...

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

\log_{2} \left(\dfrac{P}{{P}_{0}}\right)

, where

{P}_{0}

is a constant. When the metal surface is at a temperature of

487 ° C

, 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 ° C

Correct answer

Step-by-step solution

P = eA\sigma{T}^{4}

where

T

is in kelvin

\log_{2} \dfrac{eA\sigma{\left(487 + 273\right)}^{4}}{{P}_{0}} = 1

.....(i)

\log_{2} \dfrac{eA\sigma{\left(2767 + 273\right)}^{4}}{{P}_{0}} = x

......(ii)

(ii) - (i)

\log_{2} {\left(\dfrac{3040}{760}\right)}^{4} = x - 1

∴

x = 9

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