Question

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.

Answer 1

Answer:

2124.03764889 K

Explanation:

Luminosity of Sun = L

New luminosity of Sun = 3000L

$T_1$ = Current temperature of Earth = 287 K (assumed)

Luminosity is given by

$L=4\pi r^2\sigma T^4$

Here,

$L\propto T$

$\dfrac{3000L}{L}=\dfrac{T_2^4}{T_1^4}\\\Rightarrow 3000=\dfrac{T_2^4}{T_1^4}\\\Rightarrow 3000^{\dfrac{1}{4}}=\dfrac{T_2}{T_1}\\\Rightarrow T_2=3000^{\dfrac{1}{4}}\times 287\\\Rightarrow T_2=2124.03764889\ K$

The temperature of the Earth's surface is 2124.03764889 K