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

`"log"_(2)(P_(1))/(P_(0))=1`, Therefore `(P_(1))/(P_(0))=2`
According to Stefan’s law, `PpropT^(2)`
`rArr(P_(2))/(P_(1))=((T_(2))/(T_(1)))^(4)=((2767+273)/(487+273))^(4)=4^(4)`
`(P_(2))/(P_(1))=(P_(2))/(2P_(0))=4^(4),(P_(2))/(P_(0))=2xx4^(4),"log"_(2)(P_(2))/(P_(0))="log"_(2)[2xx4^(4)]`
`="log"_(2)2+"log"_(2)4^(4),"log"(P_(2))/(P_(0))=1+"log"_(2)2^(8)=9`