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scZoUnD [109]
3 years ago
6

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?
Physics
1 answer:
natka813 [3]3 years ago
6 0

Answer:

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:

P=\sigma A T^4

where

\sigma 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:

I \propto T^4

So in our problem we can write:

I_1 : T_1^4 = I_2 : T_2^4

where

I_1 = 1400 W/m^2 is the power per unit area of the present sun

T_1 = 5800 K is the temperature of the sun

I_2 is the power per unit area of sun X

T_2 = 2864 K is the temperature of sun X

Solving for I2, we find

I_2 = \frac{I_1 T_2^4}{T_1^4}=\frac{(1400 W/m^2)(2864 K)^4}{(5800 K)^4}=83.2 W/m^2

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