Sunlight arrives at the earth at the rate of . − when the sun is directly overhead. The average radius of the earth’s orbit is about . × and the radius of the sun is about . × . Estimate the surface temperature of the sun, if it is a blackbody. Take Stefan – Boltzmann constant = . × − / .
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Explanation:
The energy radiated from a blackbody from Stefan's law is E=σAT
4
For sun E=4πR
2
σT
4
where σ=5.67∗10
−8
is Stefan's constant, T is the surface temp of the blackbody in Kelvin and A is the surface area of the blackbody.
The solid angle subtended by a unit surface area on earth's surface at sun's center is dΩ=
4πr
2
1
where r is the distance from sun's center to earth.
Given,
E∗dΩ=1400
R=7∗10
8
r=1.5∗10
11
4πR
2
σT
4
∗
4πr
2
1
=
r
2
R
2
∗σT
4
=1400
∴T
4
∗
2.25
49
∗10
−6
∗5.67∗10
−8
=1400
∴T
4
=.1134∗10
16
∴T=5.83∗10
3
=5830
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