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JEE Advanced Model Paper 1 with solutions for online practice
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© examsnet.com
Question : 14
Total: 60
The solar constant which is the intensity of radiation from sun on the surface of the planet is 'S'. The surface temperature of the sun is 'T' Kelvin. If the Sun subtends a very small angle 'θ' at the planet, then the relation /s which are approximatelytrue in the following options is / are
S ∝
T
4
S ∝
T
2
S ∝
θ
2
S ∝
θ
Validate
Solution:
Power radiated from the sun Q = σeA
T
4
= (4π
a
2
)σ
T
4
where a- radius of the sun and for sun, e = 1
solar constant S =
Q
A
′
=
Q
4
π
b
2
where b - mean distance of the planet from the sun .
∴ S =
σ
.
4
π
a
2
T
4
4
π
b
2
= σ .
(
a
b
)
2
= σ
(
θ
2
)
2
.
T
4
Where Tan
(
θ
2
)
= a/b ⇒
θ
2
=
a
b
∴ S α
θ
2
α
T
4
© examsnet.com
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