contestada

During its final days as a red giant, the Sun will reach a peak luminosity of about 3000LSun. Earth will therefore absorb about 3000 times as much solar energy as it does now, and it will need to radiate 3000 times as much thermal energy to keep its surface temperature in balance. Estimate the temperature Earth’s surface will need to attain in order to radiate that much thermal energy.

Respuesta :

boffeemadrid

Answer:

2124.03764889 K

Explanation:

Luminosity of Sun = L

New luminosity of Sun = 3000L

[tex]T_1[/tex] = Current temperature of Earth = 287 K (assumed)

Luminosity is given by

[tex]L=4\pi r^2\sigma T^4[/tex]

Here,

[tex]L\propto T[/tex]

[tex]\dfrac{3000L}{L}=\dfrac{T_2^4}{T_1^4}\\\Rightarrow 3000=\dfrac{T_2^4}{T_1^4}\\\Rightarrow 3000^{\dfrac{1}{4}}=\dfrac{T_2}{T_1}\\\Rightarrow T_2=3000^{\dfrac{1}{4}}\times 287\\\Rightarrow T_2=2124.03764889\ K[/tex]

The temperature of the Earth's surface is 2124.03764889 K

Cricetus

The Earth’s surface temperature which need to attain throughout the order to radiate that much thermal energy will be "2124.04 K".

Thermal energy and Luminosity

According to the question,

Let,

Sun's luminosity be "L".

Sun's new luminosity = 3000 L

Earth's current temperature, T₁ = 287 K

We know the relation,

→ L ∝ T

or,

→ [tex]\frac{3000}{L} =\frac{T_2^4}{T_1^4}[/tex]

then,

3000 = [tex]\frac{T_2^4}{T_1^4}[/tex]

By applying cross-multiplication,

      T₂ = [tex]3000^{\frac{1}{4} }[/tex] × 287

           = 2124.03764889 K or,

           = 2124.04 K

Thus the above answer is correct.

Find out more information about thermal energy here:

https://brainly.com/question/19666326

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