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Help with Life expectancy of Main Sequence stars.

  1. Nov 5, 2008 #1
    If the nuclear fusion reaction of converting 4 H ! He occurs at an
    efficiency of 0.7%, and that mass is converted into energy according
    to the equation E = mc2, then estimate the Main Sequence lifetime
    of the Sun (spectral type G2) in years if the luminosity of the Sun is
    3.83×1033 ergs s−1. Assume the Sun’s core (10% of the total mass) is
    converted from H into He. The Sun’s mass is M⊙ = 1.9891 × 1033 g.

    t=1/M^2.5

    t=1/(91.9891x10^32)^2.5
    t= the wrong answer.

    What are we doing wrong?
     
  2. jcsd
  3. Nov 5, 2008 #2

    mathman

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    I have no particular knowledge relating to your question. However, your expression for t leads to a t with dimension g^-2.5. Since t is supposed to be in years, I presume that there must be, at a minimum, a conversion constant of some sort.
     
  4. Nov 5, 2008 #3
    That could be the wrong equation altogether...
     
  5. Nov 5, 2008 #4

    Chronos

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    The life expectancy of a main sequence star is inversely proportional to it's mass - i.e., large stars live fast and die hard, tiny brown dwarfs live dang near forever.
     
  6. Nov 7, 2008 #5
    Assuming that this is just a homework assignment, what you must do is use Einstein’s equation to determine the amount of mass you get from 3.83×10^33 ergs/second(or rather 3.83 x 10^33 erg/s=mass x c^2, and solve for the mass). BTW, according to the value in the Wiki, this should be 3.85 x 10^33 ergs/sec, but its your homework :). Then divide the Sun’s core mass (which is described as 10% of the value you are given or .1989 x 10^33 grams) by this figure. This is how many seconds it takes to convert the core’s H into He. Finally, just convert seconds to years.
    However, the Sun isn’t just going to fuse itself out of existence. It will eventually become a White Dwarf star and remain so for perhaps more than 10^100 years.
     
    Last edited: Nov 7, 2008
  7. Nov 7, 2008 #6

    tony873004

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    There's a nice "car" analogy to this problem. Your gas tank holds 20 gallons. You burn 2 gallons per hour. How long until you run out of gas? It's really the same question.
     
  8. Nov 7, 2008 #7

    Chronos

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    Fusion in small stars is a much more efficient process compared to large stars.
     
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