PLEASE ONLY USE THE INFORMATION PROVIDED. The Missing Source of the Sun\'s Energ

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PLEASE ONLY USE THE INFORMATION PROVIDED.

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 epsilon_thermal = 3P/2. (a) Using the Sun's central pressure that you calculated in question 3, what is the thermal energy density, epsilon_thermal = 3P_c/2? In the previous question we saw that the radiation energy density is epsilon_rad = aT^4 (recall that a = 7.56 times 10^-15 erg cm^-3 K^-4). What is the ratio of the thermal energy density to the radiation energy density, epsilon_thermal/epsilon_rad assuming a central temperature of T_C= 1.5 times 10^7 K? (Notice that the thermal energy density is much larger than the radiation density.) The thermal energy in the Sun acts as a reservoir for new photons. Let us imagine that the thermal reservoir is the only source of new photons which leak out of the Sun. Let's find out how long the Sun could shine. (b) Recall from the previous question that a photon created a the center of the Sun takes 3R_S^2/(lc) amount of time to randomly walk out. How many years does a photon's random walk take? (c) Since the thermal energy density content is epsilon_thermal/epsilon_rad times greater than the radiation energy density, the Sun would radiate away all its thermal energy in time epsilon_thermal/epsilon_rad times 3R_S^2/(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 times 10^9 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!

Explanation / Answer

5. 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

    C) time taken to exhaust all of the photons = time*ratio =846.654 * 30721.46119 years = 26010448 years

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