The energy from the sun reaches just outside the earth's atmoshphere at a rate of `1400 W m^(-2)` . The distance between the sun and the earth is ` 1.5 xx 10^(11) m`. (a) Calculate the rate at which the sum is losing its mass. (b) How long will the sun last assuming a constant decay at this rate? The present mass of the sun is `2 xx 10^(30) kg`

Explanation

` l = 1400 W / m^(2) `
`Power = 1400 W / m^(2) xx A `
` = (1400 xx 4 pi R^(2) ) W `
` = 1400 xx 4 pi xx (1.5 xx 10^(11))^(2) `
`= 1400 xx 4 pi xx (1.5)^(22) W`
(a) E / t = Delta m / t = E = t / c^(2) `
` 1400 xx 4 pi xx 2.25 xx 10^(22) / 9 xx 10^(16) `
` = (1400 / 4 pi xx 2.25 / 9 ) xx 10^(6) `
` = 4.4 xx 10^(9) kg/s. `
(b) ` = 4 . 4 xx 10^(9) Kg disintergrates in 1 sec .
` 2 xx 10^(-30) kg` disintegrates in ` 2 xx 10^(10) / 4.4 xx 10^(9) sec. `
` = (1 xx 10^(21) / 2.2 xx 365 xx 24 xx 3600 ) `
` = 1.44 xx 10^(-8) xx 10^(21) `
` 1.44 xx 10^(13) y `