Question

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.

• A. $16:1$
• B. $1:4$
• C. $12:1$
• D. $1:12$

Answer 1

Answer: (D)

$1:12$

Answer 2

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