Question

A black body is at temperature \(827^{\circ}\text{C}\). The rate at which it emits energy is proportional to

• A. \((827)^4\)
• B. \((827)^2\)
• C. \((1100)^4\)
• D. \((1100)^2\)

Hint:

Stefan's law needs the absolute temperature, so convert Celsius to Kelvin.

Answer 1

The Correct Option is C

Step 1: Stefan's Law:
The energy emitted per second by a black body is proportional to the fourth power of its absolute temperature: \(E\propto T^4\).

Step 2: Convert the Temperature:
\(T=827+273=1100\) K.

Step 3: Result:
So \(E\propto(1100)^4\).

Step 4: Check the Other Options:
Options (A) and (B) use the Celsius value 827, which is not an absolute scale. Option (D) uses the correct temperature but the wrong power, 2. So (C) is correct.

Final Answer:
The rate is proportional to \((1100)^4\), option (C). \[ \boxed{\text{(C) } (1100)^4} \]