Question

Assuming that the earth re-emits all the radiations it receives from the sum, determine

its temperature, (for earth, e = 1.39 × 103

w/m2 , stefan's constant. = σ = 5.735 × 10–8

w/m2

k

4

)

Answer 1

Assuming that the earth re-emits all the radiations it receives from the sum, determine its temperature, (for earth, e = 1.39 × 10³ w/m2 , stefan's constant. = σ = 5.735 × 10–8 W/m²/K⁴)

solution : using formula, P = σT⁴

where P is power per unit area, σ is Stefan's constant and T is temperature.

given, P = 1.39 × 10³ W/m²

σ = 5.735 × 10^-8 W/m²/K⁴

so, 1.39 × 10³ = 5.735 × 10^-8 T⁴

⇒(1.39 × 10³/5.735 × 10^-8) = T⁴

⇒0.242 × 10¹¹ = T⁴

⇒T = (0.242 × 10¹¹)¼

⇒ T = 394.41K

hence, Temperature = 394.41K

Answer 2

$\huge\bold\purple{Answer:-}$

using formula, P = σT⁴

where P is power per unit area, σ is Stefan's constant and T is temperature.

given, P = 1.39 × 10³ W/m²

σ = 5.735 × 10^-8 W/m²/K⁴

so, 1.39 × 10³ = 5.735 × 10^-8 T⁴

⇒(1.39 × 10³/5.735 × 10^-8) = T⁴

⇒0.242 × 10¹¹ = T⁴

⇒T = (0.242 × 10¹¹)¼

⇒ T = 394.41K

hence, Temperature = 394.41K