Question

A primitive space heater consists of a 10.0 cm radius iron ball through which electrical current was passed in order to heat the ball, and subsequently the surrounding air. If the temperature of the iron ball is kept at 510 K, and the room temperature is 20oC, what power is radiated into the room? Assume the ball is a perfect blackbody.

A. 110W
B. 480W
C. 140W
D. 430W

Answer 1

P = 430 W

Step-by-step explanation:

As we know that net rate of heat radiation into the room is given as

`(dQ)/(dt) = \sigma A(T^4 - T_s^4)`

here we have

`\sigma = 5.67 * 10^(-8)`

`A = 4\pi r^2`

`A = 4\pi(0.10^2)`

`A = 0.125 m^2`

now we have

`P = (5.67 * 10^(-8))(0.125)(510^4 - 293^4)`

`P = 430 W`