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Math Help - How can I get this equation?

  1. #1
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    How can I get this equation?

    I need to get dp/p = -a*dT + k*dP.
    I have k = -1/V * (δV/δP)
    a = 1/V * (δV/δt), a = -1/p * (δp/δT) and p = N/V
    Note that p does not equal P.
    I'm still working on this, but I'm not making much progress.
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  2. #2
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    Re: How can I get this equation?

    Hey Shanter.

    For dV/dP, use the fact that V=N/p and differentiate (you will have to use the quotient rule if N is not independent from P) which will give something in terms of p.
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  3. #3
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    Re: How can I get this equation?

    so if N is not independent than do I get (p(dN/dp) - N)/p^2? I don't see how that helps
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  4. #4
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    Re: How can I get this equation?

    The point is to get rid of the V's and the other terms not in the expression so you can collect and simplify the terms.

    Also I think you can assume N to be indepedent which simplifies things greatly and my reasoning is that if it wasn't it would be labelled N(p) or the expression would be simplified to some grand function of p.
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  5. #5
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    Re: How can I get this equation?

    Ok I think I got it now, but I'm not sure about some of the math. I get dp/p = -dV/V from dV/dp of V=N/p. Using a = 1/V * (δV/δt) i get δV = V*a*dT and using k = -1/V * (δV/δP) I get δV = -V*dP*k.
    So can does dV = δV+δV here? I get the right answer, but that doesn't feel right to me.
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