Calculate the temperature at which a perfect black body radiates at the rate of 1 W cm- 2 , Value of Stefan's constant, σ =5.67× 10- 5 erg s- 1 cm- 1 K- 4 .

Question

Calculate the temperature at which a perfect black body radiates at the rate of 1 W cm- 2 , Value of Stefan's constant, σ =5.67× 10- 5 erg s- 1 cm- 1 K- 4 . (A) 576K (B) 648K (C) 695K (D) 766K

Tardigrade Admin · Accepted Answer

Here, σ =5.67× 10- 5ergs- 1cm- 1K- 4 ; E=1Wcm- 2=107ergs- 1cm- 2 Let T be the temperature of the perfect black body. â Now, E =σ T 4 or T =(( E /σ))1 / 4 ∴ T=((107/5.67 × 10-5))1 / 4=648 K

Q. Calculate the temperature at which a perfect black body radiates at the rate of $1 W c m^{- 2}$ , Value of Stefan's constant, $σ = 5.67 \times 1 0^{- 5} er g s^{- 1} c m^{- 1} K^{- 4}$ .

$576 K$

$648 K$

$695 K$

$766 K$

Here, $σ = 5.67 \times 1 0^{- 5} er g s^{- 1} c m^{- 1} K^{- 4}$ ;
$E = 1 W c m^{- 2} = 1 0^{7} er g s^{- 1} c m^{- 2}$
Let $T$ be the temperature of the perfect black body.
Now, $E = σ T^{4}$ or $T = (\frac{E}{σ})^{1/4}$
$∴ T = (\frac{1 0 ^{7}}{5.67 \times 1 0 ^{- 5}})^{1/4} = 648 K$

Q. Calculate the temperature at which a perfect black body radiates at the rate of 1Wcm−2 , Value of Stefan's constant, σ=5.67×10−5ergs−1cm−1K−4 .

576K

648K

695K

766K