Once our Sun was about 13 million years old and had reached a temperature of app

Question

Once our Sun was about 13 million years old and had reached a temperature of approximately 10 Kelvin, a special process was about to take place. The luminosity also settles down to around 4 1026watts. It is during this time that the process of fusing hydrogen takes place, two atoms of hydrogen coming together to produce helium A. How many reaction cycles per second was our Sun fusing hydrogen in order to release enough energy to radiate 4 × 1026watts? (Hints. Each fusion reaction cycle yields 4. 3 × 10-12Joules, and Watt is a unit of power- Joules/second], and you are wanting to find a number of units [1/seconds].) B. If each reaction cycle yields 4.3 × 10-12,oules, how much mass per second is the Sun converting into energy? (hint: use Einstein's equation E-mc2 and solve for mass, E-energy for each reaction cycle, M = mass in kilograms, c = speed of light 3 × 108 meters/second]; note that units of Joules- converted /reaction). Then you can multiply that number by what you found in D., which was (# reactions/second) ending up with (mass/second). g-Tm this will give you (mass C. Explain why the Sun is at equilibrium during this phase of main sequence.

Explanation / Answer

A. Each fusion reaction yields = 4.3x10-12 joules

1 watt = 3,600 joules per hour

4x1026 watt= 4x1026x 3,600 joules per hour

4x1026 watt= 144x1028 joules per hour or (144x1028 /60)joules per second = 2.4x1028joules per second

Number of fusion reaction to yield 2.4x1028joules per second = (2.4x1028)/(4.3x10-12)

Number of fusion reaction to yield 4x1026 watt or 2.4x1028joules per second =5.5813x1039 reactions

B.

Mass per second that sun is converting into energy= mc2

4.3x10-12= m(3x108)2

Mass per second that sun is converting into energy, m=4,777.7778kg

Mass per second that sun is converting to yield 4x1026 watt= 5.5813x1039 x 4,777.7778= 2.666x1043 kg

C. Sun is in equilibrium because it has enormous volume of hrdrogen gas and hence proton-proton (hydrogen nucleus - hydrogen nucleus) chain reaction can take place for million of years to give us this energy in the form of light and heat.

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