A black body at a temperature of 227 ° C radiates heat at the rate of 5 cal cm- 2 s- 1 . At a temperature of 727 ° C the rate of heat radiated per unit area in cal cm- 2s- 1 is

Question

A black body at a temperature of 227 ° C radiates heat at the rate of 5 cal cm- 2 s- 1 . At a temperature of 727 ° C the rate of heat radiated per unit area in cal cm- 2s- 1 is (A) 400 (B) 80 (C) 40 (D) 15

Tardigrade Admin · Accepted Answer

According to Stefan's law 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 ie

E \propto T^{4}

\Rightarrow

\frac{E _{1}}{E _{2}} = \frac{T _{1}^{4}}{T _{2}^{4}}

\frac{5}{E _{2}} = \frac{( 273 + 227 ) ^{4}}{( 273 + 727 ) ^{4}}

E_{2} = 5 \times [\frac{1000}{500}]^{4}

=

5 \times 16 = 80 c a l c m^{- 2} s^{- 1}

Q. A black body at a temperature of $227^{\circ} C$ radiates heat at the rate of $5 c a l$ $c m^{- 2} s^{- 1}$ . At a temperature of $727^{\circ} C$ the rate of heat radiated per unit area in $c a l c m^{- 2} s^{- 1}$ is

$400$

$80$

$40$

$15$

Q. A black body at a temperature of 227∘C radiates heat at the rate of 5cal cm−2s−1 . At a temperature of 727∘C the rate of heat radiated per unit area in calcm−2s−1 is

400

80

40

15

Q. A black body at a temperature of $227^{\circ} C$ radiates heat at the rate of $5 c a l$ $c m^{- 2} s^{- 1}$ . At a temperature of $727^{\circ} C$ the rate of heat radiated per unit area in $c a l c m^{- 2} s^{- 1}$ is

$400$

$80$

$40$

$15$