Question

A rectangular block of surface area A emits energy E per second at \(27^{\circ} \mathrm{C}\). If length and breadth is reduced to half of initial value and temperature is raised to \(327^{\circ} \mathrm{C}\) then energy emitted per second becomes

• A. 2 E
• B. 4 E
• C. E
• D. 8 E

Hint:

Radiated power is proportional to surface area and to the fourth power of absolute temperature.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
By Stefan's law, energy emitted per second is \(E\propto A\,T^{4}\) with \(T\) in kelvin.

Step 2: Change in each factor
Length and breadth are halved, so the area becomes \(\dfrac{A}{4}\).
Temperature changes from \(27^{\circ}\text{C}=300\text{ K}\) to \(327^{\circ}\text{C}=600\text{ K}\), so \(T\) doubles.

Step 3: Calculation
\(\dfrac{E'}{E}=\dfrac{1}{4}\times 2^{4}=\dfrac{16}{4}=4\)

Final Answer:
The energy emitted per second becomes 4E. \[ \boxed{\text{(B) }4E} \]