A wire of length 1 m and radius `10^-3`m is carrying a heavy current and is assumed to radiate as a black body. At equilibrium, its temperature is 900 K while that of surrounding is 300 K. The resistivity of the material of the wire at 300 K is `pi^@xx10^-8` ohm m and its temperature coefficient of resistance is `7.8xx10^(-3)//C` (stefan's constant`sigma=5.68xx10^-8W//m^(2) K^(2)`.
Heat radiated per second by the wire is nearly

Options

A. 23 W
B. 230 W
C. 2300 W
D. 23000 W

Answer

B

Explanation

Heat radiated per second, `E=sigmaA(T^4-T_0^4)`
`=sigma(2pirl)(T^4-T_0^4)`
`=5.68xx10^-8xx2pixx10^-3xx1[(900^4-300^4)]`
`=11.36pi(6480)xx10^-3approx230W`