Question

A spherical ball of surface area 20 $c{m}^2$ absorbs any radition that falls on it. It is suspended in a closed box maintained at ${57}^0$ C. (a) Find the amoutn of radiation falling on the ball per second. (b) Find the net rate of heat flow to or from the ball at an instant when its temperature is ${200}^0$C. Stefan constant = $6.0\times {10}^{-8}W{m}^{-2}{K}^{-4}$.

Answer 1

(a) A = 20 $c{m}^2=20\times {10}^{-4}{m}^2$,

T = ${57}^0$ C = 57+273 = 330 K

E = $A\sigma T^4$

= $20\times {10}^{-4}\times 6\times {10}^{-8}\times (330{)}^4$

= 1.42 J.

(b) $\frac{E}{t}=\left(A\sigma e\right)(T_1^4-T_2^4)$

[A = $20c{m}^2=20\times {10}^{-4}{m}^2,\sigma =6\times {10}^{-8}$

$t^1=473K,t^2=330K$

= $20\times {10}^{-4}\times 6\times {10}^{-8}$
$\times 1\left[\right(473{)}^4-\left(330{)}^4\right]$

= $20\times 6\times {10}^{-12}$

[5.005 $\times {10}^{10}-1.185\times {10}^{10}]$

= $20\times 6\times 3.82\times {10}^{-2}$

= 4.58 W from the ball.