Question

A black body, at a temperature of $227^{\circ }C$, radiates heat at a rate of $20cal{m}^{-2}{s}^{-1}.$ When its temperature is raised to $727^{\circ }C$, the heat radiated by it in $cal{m}^{-2}{s}^{-1}$ will be closest to

• A. 40
• B. 160
• C. 320
• D. 640

Answer 1

Answer: (C)

The temperature of the black body is
$T_1=227^{\circ }C=500K$
$\therefore$ Using Stefan's law, the rate of heat radiation per unit area per unit time is
$E_1=\sigma T^4\Rightarrow 20=\sigma (500{)}^4$
$\Rightarrow \sigma =\frac{20}{(500{)}^4}$
Now the temperature of the blackbody is raised to
$T_2=727^{\circ }C=1000K$
$\therefore$ Rate of heat radiation per unit area
$E_2=\sigma T_2^4$
$\Rightarrow \frac{20}{(500{)}^4}\times (1000{)}^4$
$=20\times 2^4=320cal{m}^{-2}{s}^{-1}$