Question

1)a radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface is ?
2)If the temperature of the sun were to increase from T to 2T and its radius from R to 2R , then the ratio of the radiant energy received on the earth to what is was previously will be?
3)Assuming the sun to be spherical body of radius R at a temperature T K , evaluate the total radiant power , incident on earth , at a distance r from the sun?

Answer 1

1)    E = p c
       p  = E/ c    momentum transferred
2)    Energy power emitted by a black body as per Stefan-Boltzmann's law
          Energy power per unit area of surface = σ T⁴
         [ P2 / 4π (R2)² ] / [ P1 / 4π R1²]   =   T2⁴ / T1⁴
         P2 / P1 = R2² T2⁴ / [R1² * T1⁴]  = 2² * 2⁴ = 64
            64 times

3)    Power of light energy emitted per unit area from surface of Sun
         P = σ T⁴   ,   σ = Stefan Boltzmann constant = 5.67 *10⁻⁸ W/m²/K⁴
        Intensity = Power falling on unit area
        Power per unit area at distance r from Sun:
            = σ T⁴ * 4πR² /(4πr²)
            = σ T⁴ * R²/r²
       Light falling from Sun falls on Earth, on an area equal to π (R_e)² where R_e is radius of Earth. As Earth is seen as  a circular disc at distance r from the Sun.

        Total power incident on Earth = σ T⁴ R² (R_e)² /r²