Question

A certain star has a temperature twice that of the Sun and a luminosity 61 times greater than the solar value. What is its radius, in solar units?

Answer 1

We can use the Stephan-Boltzmann Law to relate the temperature (T), size (R), and luminosity (L) of a star to each other. The radius of the star (R) is related to luminosity (L) and temperature (T) through the relation

`R = (√(L))/(T^2)`

If the temperature of the star is twice times the sun and 64 times the luminosity of our sun we have that

`T= 2T_(sun) \rightarow 2units`

`L = 61L_(sun) \rightarrow 61units`

Replacing we have

`R = (√(61))/(2^2)`

`R = 1.95` solar units

Therefore the radius is 1.95 solar units.