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The intensity of solar radiation reachin...

The intensity of solar radiation reaching the illuminated side of the Earth each second is `J = 1.36 kW//m^2`. Find the docrease in the internal energy and the muss of tho Sun per second. How long will it take for the Sun's mass to decrease due to radiation by `10%` ? The volume of the Sun is to be assumed to remain constant.

Text Solution

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The correct Answer is:
`3.8xx10^(26) W; 4.2 xx10^(9) kg//s; 1.5 xx10^(12) ` years `= 4.7 xx10^(9) s`
Multiplying the solar constant by the area of a sphere of radius equal to the astronomical unit, we obtain the total power of solar radiation `P= 4piJR^2` . The loss of mass per second in `mu=P//c^2` The Sun will lose ten percent of its mass in the time
`tau=(0.1M_(o.))/mu=(M_(o.)c^2)/(40piJR^2)`
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Knowledge Check

  • When the centre of earth is at a distance of 1.5 xx 10^(11)m from the centre of sun, the intensity of solar radiation reaching at the earth's surface is 1.26kW//m^(2) . There is a spherical cloud of cosmic dust, containing iron particles. The melting point for iron particles in the cloud is 2000 K. Find the distance of iron particles from the centre of sun at which the iron particle starts melting. (Assume sun and cloud as a black body, sigma = 5.8 xx 10^(-8) W//m^(2)K^(4)) :

    A
    `2.81 xx 10^(5)m`
    B
    `2.81 xx 10^(10)m`
    C
    `2.81 xx 10^(9)m`
    D
    `1.40 xx 10^(10)m`

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