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  • A black body at 227°C radiates heat at the rate of 7 Cals/cm2s. At a temperature of 727°C, the rate of heat radiated in the same units will be:<strong

A black body at 227°C radiates heat at the rate of 7 Cals/cm2s. At a temperature of 727°C, the rate of heat radiated in the same units will be:

Option: 1

50


Option: 2

112


Option: 3

80


Option: 4

60


Answers (1)

best_answer

Heat energy per unit time= $\quad R=\sigma A e T^{4}$
Thus heat energy per unit area= $\quad R^{\prime}=\sigma e T^{4}$
\Rightarrow \quad \frac{R_{2}^{\prime}}{R_{1}^{\prime}}=\left(\frac{T_{2}}{T_{1}}\right)^{4}$

The initial temperature of the body $\quad T_{1}=227^{\circ} \mathrm{C}=(227+273) K=500 \mathrm{K}$
The final temperature of the body $\quad T_{2}=727^{\circ} \mathrm{C}=(727+273) K=1000 \mathrm{K}$
\therefore \quad \frac{R_{2}^{\prime}}{7}=\left(\frac{1000}{500}\right)^{4}$

\frac{R_{2}^{\prime}}{7}=16$

$\Rightarrow R_{2}^{\prime}=112 \quad \mathrm{cal} / \mathrm{cm}^{2}$.s

Posted by

Divya Prakash Singh

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