Question

A black body, at a temperature of $227^{\circ} C$, radiates heat at a rate of $20 \,cal\, m ^{-2} s ^{-1} .$ 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
$T _{1}=227^{\circ} C =500\, K$
$\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
$T _{2}=727^{\circ} C =1000 \,K$
$\therefore $ Rate of heat radiation per unit area
$E_{2}=\sigma T_{2}^{4}$
$ \Rightarrow \frac{20}{(500)^{4}} \times(1000)^{4}$
$=20 \times 2^{4}=320\, cal\, m ^{-2} s ^{-1}$