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Math Help - Maxwell-Boltzmann law-urgent

  1. #1
    Yan
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    Maxwell-Boltzmann law-urgent

    According to the Maxwell-Boltzmann law of theoretical physics, the probability density of V, the velocity of a gas molecule, is
    f(v)=kv^2*e^(- βv^2), for v>0; =0, elsewhere.
    Where β depends on its mass and the absolute temperature and k is an appropriate constant. Show that the kinetic energy E=(1/2)mV^2, where m the mass of the molecule is a random variable having a gamma distribution.
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  2. #2
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    Quote Originally Posted by Yan View Post
    According to the Maxwell-Boltzmann law of theoretical physics, the probability density of V, the velocity of a gas molecule, is
    f(v)=kv^2*e^(- βv^2), for v>0; =0, elsewhere.
    Where β depends on its mass and the absolute temperature and k is an appropriate constant. Show that the kinetic energy E=(1/2)mV^2, where m the mass of the molecule is a random variable having a gamma distribution.
    Follow the method shown in this thread: http://www.mathhelpforum.com/math-he...functions.html

    If you still have trouble after reading this, please show your working and where you get stuck.
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  3. #3
    Yan
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    Quote Originally Posted by mr fantastic View Post
    Follow the method shown in this thread: http://www.mathhelpforum.com/math-he...functions.html

    If you still have trouble after reading this, please show your working and where you get stuck.
    The problem is i don't understand what is the question ask for..
    can you explain to me? and step by step???

    Quote Originally Posted by mr fantastic View Post
    Follow the method shown in this thread: http://www.mathhelpforum.com/math-he...functions.html

    If you still have trouble after reading this, please show your working and where you get stuck.
    In this problem, i'm confuse about the sentence<where m the mass of the molecule is a random variable having a gamma distribution.>what is the relationship between this sentence and the problem?
    Last edited by mr fantastic; March 1st 2009 at 06:55 PM. Reason: Merged posts
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    Quote Originally Posted by Yan View Post
    The problem is i don't understand what is the question ask for..
    can you explain to me? and step by step???
    You're given the pdf for V and asked to find the pdf of \frac{m}{2} V^2.

    Now read the thread I gave. If you still have trouble after reading it, please show your working and where you get stuck.
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    Yan
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    Quote Originally Posted by mr fantastic View Post
    You're given the pdf for V and asked to find the pdf of \frac{m}{2} V^2.

    Now read the thread I gave. If you still have trouble after reading it, please show your working and where you get stuck.
    G(y) = P (Y<y)
    = P ( \frac{m}{2} V^2<y)
    = 2 P(V< \sqrt{\frac{2x}{M}})
    = 2* ....

    I just confuse about the m, because in the problem, it says that m is a random variable having a gamma distribution. what is this information use for???
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  6. #6
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    Quote Originally Posted by Yan View Post
    G(y) = P (Y<y)
    = P ( \frac{m}{2} V^2<y)
    = 2 P(V< \sqrt{\frac{2x}{M}})
    = 2* ....

    I just confuse about the m, because in the problem, it says that m is a random variable having a gamma distribution. what is this information use for???
    There is a comma missing after molecule, it should read:

    "Show that the kinetic energy E=(1/2)mV^2, where m the mass of the molecule, is a random variable having a gamma distribution."

    m is not a random variable, E (the kinetic energy) is the random variable in question.

    CB
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