Spread the love

Solar Constant | What is the Solar Constant

Solar Constant (S) :- The Sun continuously sends out energy in the form of radiation. Only a small part of it reaches the Earth. It represents the average intensity of solar radiation reaching Earth from the Sun.

Definition of Solar Constant

The amount of solar energy received per unit area per unit time by a black surface held perpendicular to the Sun’s rays and placed at the mean distance of the Earth from the Sun (in the absence of atmosphere) is called solar constant.

Its approximate value is :

S = 1340 watts/m² or 1.937 Cal./cm²–minute

Calculation of Temperature of the Sun using Solar Constant

Let R = Radius of the Sun & d = Radius of Earth’s orbit around the Sun.

The Sun radiates approximately like a black body. The power emitted per unit area by the Sun’s surface is given by Stefan–Boltzmann law :

$\displaystyle {{E}_{surface}}=\sigma {{T}^{4}}$

Total Power emitted by Sun = 4πR²σT⁴

This power spreads out uniformly over a sphere of radius equal to the Earth–Sun distance . So, the energy falling per unit area of Earth. i.e., Solar Constant (S) :

$\displaystyle S=\frac{4\pi {{R}^{2}}\sigma {{T}^{4}}}{4\pi {{d}^{2}}}=\frac{{{R}^{2}}\sigma {{T}^{4}}}{{{d}^{2}}}$

Hence temperature of the Sun :

$\displaystyle T={{\left[ \frac{S{{d}^{2}}}{\sigma {{R}^{2}}} \right]}^{\frac{1}{4}}}$

Substituting values :

Solar constant

Stefan–Boltzmann constant

Solar radius

Mean Earth–Sun distance

$\displaystyle T={{\left[ \frac{1340\times {{\left( 1.5\times {{10}^{11}} \right)}^{2}}}{5.7\times {{10}^{-8}}\times {{(7\times {{10}^{8}})}^{2}}} \right]}^{\frac{1}{4}}}$

$\displaystyle \therefore T=5732K$

Solar Constant | What is the Solar Constant

Definition of Solar Constant

Calculation of Temperature of the Sun using Solar Constant

Like this: