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Monday, March 5, 2018

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

6 comments:

  1. Can you please tell where it is told that it is Power as it can be work also?
    Thank you

    ReplyDelete
  2. I thought it would be Weight instead of power. Why is it not weight?

    ReplyDelete

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