Please help: The radiation per unit area from the Sun reaching the earth is 1400

Question

Please help:

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 2434 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? Answer in units of W/m2

Explanation / Answer

radiative power is proportional to fourth power of temperature

so 1400=k*5800^4

similarly

x=k*2434^4

dividing them we get

x=1400*(2434/5800)^4=43.42W/m^2

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