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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» <html><body><p>4990.5 K<br/> 5706.8 K<br/>5903.7K<br/>6063.4 K</p>Solution :If T is surface temperature of the sun, then Energy radiated by the sun per second is<br/> `E=<a href="https://interviewquestions.tuteehub.com/tag/sigma-1207107" style="font-weight:bold;" target="_blank" title="Click to know more about SIGMA">SIGMA</a> T^4 <a href="https://interviewquestions.tuteehub.com/tag/xx-747671" style="font-weight:bold;" target="_blank" title="Click to know more about XX">XX</a> <a href="https://interviewquestions.tuteehub.com/tag/4pi-1882352" style="font-weight:bold;" target="_blank" title="Click to know more about 4PI">4PI</a> R^<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>` <br/>where R is the radius of the sun, then This energy spreads over a sphere of radius r, <br/>` therefore `E = <a href="https://interviewquestions.tuteehub.com/tag/rate-1177476" style="font-weight:bold;" target="_blank" title="Click to know more about RATE">RATE</a> of radiation incident on earth. surface ` xx 4pi r^2` <br/>`rArr sigma T^4 xx4pi R^2 = 1500 xx 4pi r^2` <br/> ` T^4 = (1500 xx r^2)/(sigma R^2)` <br/> ` = (1500 xx (15 xx 10^10)^2)/(5.67 xx 10^(-8) xx (7 xx 10^8)^2)` <br/> ` T = ( (15 xx 2.25)/(5.67 xx 49) )^(1/4) xx 10^4= 59903.7 K`</body></html>


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