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.

Question

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. (A)  16:1  (B)  1:4  (C)  12:1  (D)  1:12

Tardigrade Admin · Accepted Answer

(P1/P2)=(σ A1 T12/σ A2 T22) ∴ (A1/A2) =(P1/P2) ×((T2/T1))4 =(20/15)((500/1000))4 =(1/12)

Q. A black body emits heat at the rate of $20 W$ . When its temperature is $72 7^{\circ} C$ . Another black body emits heat at the rate of $15 W$ , when its temperature is $22 7^{\circ} C$ . Compare the area of the surface of the two bodies, if the surrounding is at NTP.

$16 : 1$

$1 : 4$

$12 : 1$

$1 : 12$

$\frac{P _{1}}{P _{2}} = \frac{σ A _{1} T _{1}^{2}}{σ A _{2} T _{2}^{2}}$
$∴ \frac{A _{1}}{A _{2}} = \frac{P _{1}}{P _{2}} \times (\frac{T _{2}}{T _{1}})^{4}$
$= \frac{20}{15} (\frac{500}{1000})^{4}$
$= \frac{1}{12}$

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

16:1

1:4

12:1

1:12