Estimate the temperature of the surface of the sun from the following

1.	Estimate the temperature of the surface of the sun from the following data:(i) Average radius of the earth’s orbit= 1.5 × 105 km(ii) Average radius of the sun= 7.0 × 105 km(iii) Solar radiant power on the earth= 1400 Wm-2 at noon timeAssume the sun to be a perfect black body will your estimate be greater or less than the actual surface temperature of the sun? Explain.
Answer» Here, Radius of Sun R = 7 × 10⁵ km = 7 × 10⁸ m ∴ Surface area of sun = 4πR² = 4π(7 × 10⁸)² = 6.16 × 10¹⁸m² σ = 5.67 × 10^-8 Wm^-2 K^-4 Using E = AσT⁴ , E = (6.16 × 10¹⁸)(5.67 × 10^-8 )T4 = 3.49 × 10¹¹ × T⁴W E = 4πr^r × Solar radiant power on earth Here, Radius of Earth = r = 1.5 × 10²⁵ km = 1.5 × 10⁸ m E = 4π(1.5 × 10⁸)² × 1400 = 3.96 × 10²⁰ watt Then equating 3.49 × 10¹¹ × T⁴ = 3.96 × 10²⁰ T⁴ = \(\frac{3.96\times10^{20}}{3.49\times10^{11}}\) T = 1.83 × 10² K.

Estimate the temperature of the surface of the sun from the following data:(i) Average radius of the earth’s orbit= 1.5 × 105 km(ii) Average radius of the sun= 7.0 × 105 km(iii) Solar radiant power on the earth= 1400 Wm-2 at noon timeAssume the sun to be a perfect black body will your estimate be greater or less than the actual surface temperature of the sun? Explain.

Answer»

Here, Radius of Sun R = 7 × 10⁵ km

= 7 × 10⁸ m

∴ Surface area of sun = 4πR²

= 4π(7 × 10⁸)²

= 6.16 × 10¹⁸m²

σ = 5.67 × 10^-8 Wm^-2 K^-4

Using E = AσT⁴ ,

E = (6.16 × 10¹⁸)(5.67 × 10^-8 )T4

= 3.49 × 10¹¹ × T⁴W

E = 4πr^r × Solar radiant power on earth

Here, Radius of Earth = r = 1.5 × 10²⁵ km = 1.5 × 10⁸ m

E = 4π(1.5 × 10⁸)² × 1400

= 3.96 × 10²⁰ watt

Then equating

3.49 × 10¹¹ × T⁴ = 3.96 × 10²⁰

T⁴ = \(\frac{3.96\times10^{20}}{3.49\times10^{11}}\)

T = 1.83 × 10² K.