Calculate Energy Prod. in Sun, Hydrogen Consumption & Burning Time

[iuchem16]

The radiation flux from the sun at the top of the Earth's atmosphere is 0.139 J cm-2 s-1 at normal incidence. The Earth is 1.50x108 km from the sun. Calculate:
(a) the energy production in the sun in MeV/s
(b) the rate of hydrogen consumption in g/s
(c) how long hydrogen-burning can continue in the sun under the assumption that energy production continues at the present rate and that hydrogen burning will cease when 10% of the total hydrogen mass has been used up.
The mass of the sun is 2.0x1033g.

I have determined that the energy production in the sun is 2.5e39 MeV/s by converting the flux to MeV/cm^2*s and multiplying that by the area of the sphere produced by the radiation with r=1.50x108 km. However, I'm not sure how to calculate b & c. I was thinking it may have to do with the pp1 chain?

 

[mgb_phys]

For b, and c you need to know how much energy is emitted in each fusion event and how much hydrogen is consumed

 

[Blueshift5]

(a) To calculate the energy production in the sun in MeV/s, we can use the formula E=mc^2, where E is the energy produced, m is the mass of the sun, and c is the speed of light. We can convert the mass of the sun to kilograms (2.0x10^33 g = 2.0x10^30 kg) and use the value for the speed of light (c= 2.998x10^8 m/s) to get:

E = (2.0x10^30 kg)(2.998x10^8 m/s)^2 = 1.798x10^47 J/s

To convert this to MeV/s, we can use the conversion factor 1 MeV = 1.602x10^-13 J, giving us:

E = (1.798x10^47 J/s)(1 MeV/1.602x10^-13 J) = 2.5x10^39 MeV/s

(b) The rate of hydrogen consumption in g/s can be calculated using the energy production rate from part (a) and the energy released per fusion reaction in the pp1 chain. In the pp1 chain, four hydrogen nuclei (protons) fuse to form one helium nucleus, releasing a total of 26.7 MeV of energy. Therefore, the rate of hydrogen consumption can be calculated as:

Rate of hydrogen consumption = (Energy production rate)/(Energy released per fusion reaction)

= (2.5x10^39 MeV/s)/(26.7 MeV/reaction)

= 9.4x10^37 reactions/s

To convert this to grams per second, we need to know the mass of hydrogen in one reaction. One hydrogen nucleus has a mass of 1.007825 u, or 1.673x10^-27 kg. Therefore, the mass of four hydrogen nuclei is 4.0313x10^-27 kg. Using this, we can calculate the rate of hydrogen consumption in grams per second:

Rate of hydrogen consumption = (9.4x10^37 reactions/s)(4.0313x10^-27 kg/reaction)(1000 g/kg)

= 3.8x10^11 g/s

(c) To calculate how long hydrogen burning can continue in the sun, we need to know the total mass of hydrogen in the sun and the rate of hydrogen consumption