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Using Stefan-Boltzmann and Wien laws The Sun emits P = 4 1026Watts, its radius is 6.95...

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.

Expert Solution

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,

genius_generous answered 8 months ago

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