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

Question

A star 'A' has radiant power equal to 3 times that of the Sun. The temperature of star 'A' is $ 6000 \, \mathrm{K} $ and that of the Sun is $ 2000 \, \mathrm{K} $. What is the ratio of their radii?

Answer 1

Step 1: Two factors:
Area factor: $\left(\tfrac12\right)^2 = \tfrac14$. Temperature factor: $(600/300)^4 = 16$.

Step 2: Multiply:
$\tfrac14\times16 = 4$.

Step 3: Result:
The new emission is $4E$, option (B).

Final Answer:
The new energy emitted is 4E. \[ \boxed{\text{(B) }4E} \]

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

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The Correct Option is B

Solution and Explanation

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