Question

A small-blackened solid copper sphere of radius 2.5 cm is placed in an evacuated chamber. The temperature of the chamber is maintained at 100 ºC. At what rate energy must be supplied to the copper sphere to maintain its temperature at 110 ºC? 

Answer 1

Given : r = 2.5 cm = 2.5 ×10^-2m, T₀ = 273+100 = 373 K, T = 273+110 = 383 K,

σ = 5.76 × 10^-8 J s^-1 m^-2 K^-4

The rate at which energy must be supplied =

sA(T⁴- T₀⁴)= σ2πr² (T⁴- T₀⁴)

= (5.76 × 10^-8 )(2)(3.142)( 2.5 ×10^-2)²( 383⁴-373⁴)

=0.9624 W