Question

What is the dimensional formula of solar constant?

Answer 1

Hint: We can calculate the dimensional formula by putting the values of basic physical quantities in the formula.
Formula
Here we used the formula
\[\dfrac{{Energy}}{{Area \times \operatorname{Sec} ond}}\]

Complete step-by-step solution:
Solar constant is the rate at which energy reaches the earth's surface from the sun, usually taken to be 1,388 watts per square metre. Solar constant is defined as the energy incident per unit area per second
Which brings us to the formula of
\[\dfrac{{Energy}}{{Area \times \operatorname{Sec} ond}}\]
We put the dimensional formula of the physical quantities in the formula
Dimensional formula for Energy is \[{M^1}{L^2}{T^{ - 2}}\]
Dimensional formula for Area is \[{L^2}\]
Dimensional formula for Second is \[{T^1}\]
Putting these values in the formula, we get
\[\dfrac{{{M^1}{L^2}{T^{ - 2}}}}{{{L^2}{T^1}}}\]
Now we will perform basic operation like division and multiplication of same physical quantity
\[\left[ {{M^1}} \right]{\text{ }}\left[ {{L^2}{L^{ - 2}}} \right]\left[ {{T^{ - 2}}{T^{ - 1}}} \right]\]
This gives us \[\left[ {{M^1}{L^0}{T^{ - 3}}} \right]\] .
Additional Information
The solar constant includes all types of solar radiation and not just the visible light (though by convention, neutrinos, being electrically neutral, do not radiate). It is measured by satellite as being \[1.361\] kilowatts per square meter \[\left( {\dfrac{{KW}}{{{m^2}}}} \right)\] at solar minimum (the time in the 11-year solar cycle when the number of sunspots is minimal) and approximately \[0.1\% \] greater (roughly \[1.362\] \[\left( {\dfrac{{KW}}{{{m^2}}}} \right)\] at solar maximum

Note: The solar constant ${G_x}$ is a flux density measuring mean solar electromagnetic radiation (solar irradiance) per unit area. It is measured on a surface perpendicular to the rays, one astronomical unit (AU) from the Sun (roughly the distance from the Sun to the Earth).