1.

The solar constant for the earth is Σ. The surface temperature of the sun is T K. The sun subtends an angle θ at the earth.(a) Σ ∝ T4(b) Σ ∝ T2(c) Σ ∝ θ2(d) Σ ∝ θ

Answer»

Correct Answer is; (a) Σ ∝ T, (c) Σ ∝ θ2

Let R = radius of the sun, d = distance of the earth from the sun.

Power radiated by the sun = (4πR2) σT4 =P. 

Energy received per unit area per second normally on the earth 

= Σ = P/4πd2 

= 4πR2σT4 / 4πd2 

= (σT4) (R/d)2 

= 1/4 σT4 (2R/d)2

Angle subtended by the sun at the earth = θ 2R/d.

or Σ = constant x T4 x θ2.



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