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 scale that displays `log_2,(P//P_0)`, where `P_0` is 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`?

Answer

9

Explanation

`P = eAsigmaT^(4)` where `T` is in kelvin
`"log"_(2)(eAsigma(487 + 273)^(4))/(P_(0)) = 1 …..(i)`
`"log"_(2)(eAsigma(2767 + 273)^(4))/(P_(0)) = x ….. (ii)`
(ii) - (i)
`"log"_(2) ((3040)/(760))^(4) = x-1`
`therefore x = 9`