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 displyed by the sensor when the temperature of the metal surface is raised to `2767^@C`?

Explanation

(9) Here `p prop T^4 or P=P_0T^4`
`:. log _2P=log _2P_0+log _2T^4 :. log _2P/(P_0)=4log _2T`
At `T=487^@C=760K, log _2P/(P_0)=4log_2760=1…(1)`
At `T=2767^@C=3040K,`
`log_e rho/(rho_0)=4log _2P3040=4log _2(760xx4)`
`=4[log _2760+log _2 2^2]`
`=4log _2760+8=1+8=9`