Question

The Missing Source of the Sun’s Energy: As photons from the Sun’s interior leak away, they are replaced with new ones. But what is the source of those new photons? In the core of the Sun, the gas is hot and thermodynamics tells us that the thermal energy per unit volume (the thermal energy density) stored in the motion of the gas particles is Ethermal = 3P/2. Since the thermal energy density content is Ethermal/Erad times greater than the radiation energy density, the Sun would radiate away all its thermal energy in time Ethermal/Erad × 3R2S/(lc). How many years would it take for the Sun to exhaust its thermal reservoir of photons? Notice how much smaller your result is compared to the geologically established age of the Earth, 4.5 × 109 years old. This problem confused nineteenth-century physicists. It’s clear that something must be replacing the thermal energy density of the Sun. The solution cannot come from classical physics!

Answer 1

Here, We cannot Take a single case, we have to take it from the Starting parts,

a) Pc ( central pressure) = 2.16024*10^17 Barye
E-thermal = 3Pc/2 = 3.24036*10^17 Barye
E-rad = aT^4 = 7.56*10^-15 * (1.5*10^7)^4 = 3.8275*10^14 Barye
E-thermal/E-radiation = 846.654

b) time = 3*Rs^2 / lc = 3*(6.96*10^10 )^2 / 0.5*3*10^10 = 9.68832*10^11 s = 30721.46119 years

Here, your Question, time taken to exhaust all of the photons = time*ratio =846.654 * 30721.46119 years = 26010448 years

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