1. Tardigrade
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  4. A black body emits heat at the rate of 20 W. When its temperature is 727° C. Another black body emits heat at the rate of 15 W, when its temperature is 227° C. Compare the area of the surface of the two bodies, if the surrounding is at NTP.

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Q. A black body emits heat at the rate of $20\, W$. When its temperature is $727^{\circ} C$. Another black body emits heat at the rate of $15\, W$, when its temperature is $227^{\circ} C$. Compare the area of the surface of the two bodies, if the surrounding is at NTP.

AIIMSAIIMS 2014

Solution:

$\frac{P_{1}}{P_{2}}=\frac{\sigma A_{1} T_{1}^{2}}{\sigma A_{2} T_{2}^{2}}$
$\therefore \frac{A_{1}}{A_{2}} =\frac{P_{1}}{P_{2}} \times\left(\frac{T_{2}}{T_{1}}\right)^{4}$
$=\frac{20}{15}\left(\frac{500}{1000}\right)^{4}$
$=\frac{1}{12}$