Question

A black body is at a temperature of 727°C. It emits energy at a rate which is proportional to:
1. (1000)³
2. (1000)⁴
3. (727)²
4. (727)⁴

Answer 1

Correct Answer - Option 2 : (1000)⁴

CONCEPT:

• Stefan's Law: According to it the radiant energy emitted by a perfectly black body per unit area per sec (i.e. emissive power of black body) is directly proportional to the fourth power of its absolute temperature i.e.

\(E \propto {T^4}\)

\( \Rightarrow E = \sigma {T^4}\)

Where, is a constant called Stefan’s constant.

• The value of Stefan's constant is 5.67 × 10-8 W/m2K4.

CALCULATION:

Given - Temperature of black body (T) = 727°C = 727 + 273 = 1000 K

• The radiant energy emitted by a perfectly black body per unit area per sec is

\( \Rightarrow E = \sigma {(1000)^4}\)

• The radiant energy emitted by a perfectly black body is proportional to 

\( \Rightarrow E \propto {(1000)^4}\)