Question

The rectangular surface of area 8 cm × 4 cm of a black body at a temperature of 127^0C emits energy at the rate of E per second. If the length and breadth of the surface are each reduced to half of the initial value and the temperature is raised to 327^0C, the rate of emission of energy will become

• A. $\frac{3}{8}E$
• B. $\frac{81}{16}E$
• C. $\frac{9}{16}E$
• D. $\frac{81}{64}E$

Answer 1

Answer: (D)

$\frac{81}{64}E$

Answer 2

Energy radiated by body per second $\frac{Q}{t} = A\sigma T^{4}$ or

$\frac{Q}{t} \propto l \times b \times T^{4}$ [Area = l × b]

∴$\frac{E_{2}}{E_{1}} = \frac{l_{2}}{l_{1}} \times \frac{b_{2}}{b_{1}} \times \left( \frac{T_{2}}{T_{1}} \right)^{4}$

$= \frac{1}{2} \times \frac{1}{2} \times \left( \frac{3}{2} \right)^{4}$ ⇒ $E_{2} = \frac{81}{64}E$