Consider the sun as a black body of radius `7 xx 10^8` m and the earth receiving its surface radiations from the sun at a rate of approximately `1500 W//m^2` . If the distance of the centre of the sum from the earth's surface is `15 xx 10^10` m, then the surface temperature of the sun is

Options

A. 4990.5 K
B. 5706.8 K
C. 5903.7K
D. 6063.4 K

Answer

C

Explanation

If T is surface temperature of the sun, then Energy radiated by the sun per second is
`E =sigma T^4 xx 4pi R^2`
where R is the radius of the sun, then This energy spreads over a sphere of radius r,
` therefore ` E = Rate of radiation incident on earth. surface ` xx 4pi r^2`
`rArr sigma T^4 xx 4pi R^2 = 1500 xx 4pi r^2`
` T^4 = (1500 xx r^2)/(sigma R^2)`
` = (1500 xx (15 xx 10^10)^2)/(5.67 xx 10^(-8) xx (7 xx 10^8)^2)`
` T = ( (15 xx 2.25)/(5.67 xx 49) )^(1/4) xx 10^4 = 59903.7 K`