Question

A lamp filament radiates 100 W of power when the temperature of the surroundings is 20°C and it radiates 99.5 W of power when the temperature of the surroundings is 35°C. If the temperature of the filament is the same in each case, what is that temperature on the Celsius scale?

Answer 1

here,

let the temprature of the filament be T

the temprature , T1 = 20 degree C

T1 = 293 K

the temprature , T2 = 35 degree C

T2 = 308 K

the radiated power for t1 , P1 = area * sigma *(T^4 - T1^4)

100 = area * sigma *(T^4 - 293^4) .......(1)

the radiated power for T2 , P2 = area * sigma *(T^4 - T2^4)

99.5 = area * sigma * (T^4 - 308^4) ........(2)

dividing equation (1) from (2) and solving for T

T = 759.76 K

T = 486.76 degree C

the temprature of the filament is 486.76 degree C