Consider the sun as a black body of radius 7 xx 10^8m 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

Consider the sun as a black body of radius 7 xx 10^8m and the earth re

1.	Consider the sun as a black body of radius 7 xx 10^8m 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
Answer» 4990.5 K 5706.8 K 5903.7K 6063.4 K Solution :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 xx4pi 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`