The radiation per unit area from the sun reaching the earth is 1400 w/m2 , approximately the amount of radiative power per unit area reaching a sun bather on the banks of barton springs at noon on a clear day in june. the temperature of the sun is 5800 k. now suppose instead of the present sun we received radiation from sun x at temperature 2864 k, located at the same position as our sun. how much radiative power per unit area would reach the sun bather from the new sun x?

83.2 W/m^2

Explanation:

The radiation per unit area of a star is directly proportional to the power emitted, which is given by Stefan-Boltzmann law:

where

is the Stefan-Boltzmann constant

A is the surface area

T is the surface temperature

So, we see that the radiation per unit area is proportional to the fourth power of the temperature:

So in our problem we can write:

where

is the power per unit area of the present sun

is the temperature of the sun

is the power per unit area of sun X

is the temperature of sun X

Solving for I2, we find

answer; equivalent to a one(1) horsepower motor;