The luminosity L of a star is given by L = 4πr2σT4 where r is the radius of the star

Question 5

The luminosity L of a star is given by

L = 4πr²σT⁴

where

r is the radius of the star,

T is the temperature of the star,

σ is a constant with units W m^-2 K^-4.

What are the SI base units of L?

A kg m² s^-1                        B kg m² s^-2                        C kg m² s^-3                       D kg m² s^-4

Reference: Past Exam Paper – June 2016 Paper 12 Q2

Solution:

Answer: C.

L = 4πr²σT⁴

[L] = [r²] [σ] [T⁴]

4π is a constant that has no unit. {Note that some constants may have units.}

[L] = (m²) (W m^-2 K^-4) (K⁴) = W

The unit W (watt) is not an SI base unit.

Watt is the unit of power.

Power = Work done / time = (Force × distance) / t = (ma × s) / t

Power = (ma × s) / t

[L] = W = (kg) (m s^-2) (m) / s = kg m² s^-3