How long the sun would shine if it converts all it's Hydrogen to Helium

In summary, the conversation discusses the use of hydrogen in the sun to produce energy and how to calculate the length of time the sun will continue to shine using this process. The participants consider different approaches, including using the sun's total energy and mass of hydrogen, and eventually come to an estimated answer of approximately 7.85 x 10^10 years.
  • #1
b_o3
52
0
Hello, I've got this problem:

The sun converts 1.91exp19 kg of Hydrogen to Helium per year, given that the sun started out with 75% Hydrogen by mass, computer how long the sun would shine if it converts all it's Hydrogen to Helium.

I computed the total energy of the sun as 3.81exp41 joules.

I tried subtracting the total energy of the sun from 75% of the energy from Hydrogen (computed using E=mc2) but that doesn't really add up. I computed the luminosity of the sun = 3.9exp26. I'm a little lost with this question can someone help me please.

thanks,
 
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  • #2
sorry I forgot to mention, mass of sun = 2exp30 kg, radius of sun = 7exp8 m. ... should i use GM2/R to get energy of the sun?
 
  • #3
I found total energy of sun contributed by Hydrogen = 2.14exp41 Joules...
 
  • #4
Why are you worrying about the energy of the Sun?

You know the mass of the Sun
You know what percentage of that is hydrogen.
You know how much hydrogen is used up in a year.

That's all you need to know to solve this problem.
 
  • #5
hows that going to work ?
 
  • #6
u know the mass of Sun ,hence u know the mass of hydrogen in it.

u know the mass of hydrogen used every year ,so u know how many years u can use it!
 
  • #7
b_o3 said:
hows that going to work ?

Simular problem:

Your gas tank holds 10 gals.
It is half full.
Your car uses 1/25 of a gal for every mile you drive.

How many miles can you drive on the gas in your tank?
 
  • #8
so I found mass of H in sun = 1.5 exp30 kg, I divided that by rate of Hydrogen conversion which is equal to 1.91 exp 19 kg per year, and I got 7.85 years is this the correct answer?
 
  • #9
so I found mass of H in sun = 1.5 exp30 kg, I divided that by rate of Hydrogen conversion which is equal to 1.91 exp 19 kg per year, and I got 7.85 years is this the correct answer?
 
  • #10
b_o3 said:
so I found mass of H in sun = 1.5 exp30 kg, I divided that by rate of Hydrogen conversion which is equal to 1.91 exp 19 kg per year, and I got 7.85 years is this the correct answer?

7.85 years?! Aren't you missing some zeros?
 
  • #11
but wait hows this right... the sun shines when there's energy, so I should probably use the total energy available to compute how long it will shine .. right? When I do that I get 3.93 exp 12

thanks,
 
  • #12
What does your intuition tell you about that answer? Will the sun really really run out of hydrogen in the year 2015?

Check your division. Also, the sun realistically won't burn all its hydrogen, but only about 10% of it since only the central regions get hot enough for fusion to occur.

Try 10% of 75% of the sun's mass divided by the mass it burns per year, and see if your answer is in rough agreement with the estimated main sequence lifetime of the sun from a source such as wikipedia.
 
Last edited:
  • #13
b_o3 said:
but wait hows this right... the sun shines when there's energy, so I should probably use the total energy available to compute how long it will shine .. right? When I do that I get 3.93 exp 12

thanks,

No, stay away from energy. It's a simple as Janus' explanation.
 
  • #14
how would it run out of hydrogen in 2015... i said it was 3.93 exp 12. But now the problem is I am not sure whether to use the total energy of the sun to divided by rate of conversion..or should i use the total mass of Hydrogen
 
  • #15
okay cool then .. I got 7.85 exp 10 .. which seems about right
 
  • #16
a little optimistic, but within an order of magnitude or so of current estimates using much more sophisticated analysis.
 

1. How long would the sun shine if it converts all its Hydrogen to Helium?

In simple terms, the sun would shine for approximately 5 billion years if it were to convert all its Hydrogen to Helium. This is because the sun's energy comes from the fusion of Hydrogen nuclei to form Helium, and it has enough Hydrogen fuel to sustain this process for around 5 billion years.

2. Why does the sun's conversion of Hydrogen to Helium determine its lifespan?

The sun's conversion of Hydrogen to Helium is the main source of the sun's energy. As this process progresses, the sun's core will eventually run out of Hydrogen fuel, causing the fusion process to slow down and the sun's energy output to decrease. This, in turn, will lead to the sun's death and the end of its shining.

3. Can the sun's conversion of Hydrogen to Helium be reversed?

No, the process of converting Hydrogen to Helium in the sun is a one-way process. Once the Hydrogen fuel is used up, it cannot be replaced or replenished. This is why the sun's lifespan is finite and cannot be reversed.

4. How does the sun's conversion of Hydrogen to Helium impact its size and temperature?

As the sun converts Hydrogen to Helium, it gradually increases in size and temperature. This is because the Helium produced in the fusion process takes up more space than the original Hydrogen atoms, causing the sun to expand. Additionally, the increase in temperature is due to the release of energy from the fusion process.

5. Is the sun's conversion of Hydrogen to Helium a continuous process?

Yes, the sun's conversion of Hydrogen to Helium is a continuous process that has been ongoing for billions of years. It is the main source of the sun's energy and will continue until the sun's core runs out of Hydrogen fuel, leading to its eventual death.

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