In: Physics
Using Stefan-Boltzmann and Wien laws
The Sun emits P = 4 1026Watts, its radius is 6.95 10 ^89m and its surface temperature T(Sun) = 5,800 K. We know that the Sun will gradually increase its power output in the future. We also know that its surface temperature will not change significantly, at least for a while. Using the law for the ‘black body’ radiation, find how much the Sun’s radius will change in %, if the power output of the Sun doubles.
GIVEN:
Power emitted,
Radius,
Surface Temperature of the sun,
TO FIND The radius of the sun if the power of the sun doubles.
APPROACH: From Stefan-Boltzmann law, the power radiated by the sun is given as,
where is
the surface area of the sun
is its emissivity
is called Stefan's constant
is
it's surface temperature.
SOLUTION:
From the above Stefan-Boltzmann relationship,
Cancelling the constants,
and temperatures as
Thus the percentage change in the radius of the sun is given by,