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Math Help - A Partial differetial question

  1. #1
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    A Partial differetial question

    PV = RT(1+B(T)/V)

    Code:
    
    
    
    
    
    \beta = (1/V)*(
    
    
    
    
    \frac{dV}{dT})
    at constant P

    show
    Code:
    
    
    
    
    
    \beta =
    
    
    
    
    \frac{1}{T}*
    
    
    
    
    \frac{V + B + T\frac{dB}{dT}}{V + 2B}
    I got to

    Code:
    
    
    
    
    
    \beta =
    
    
    
    
    \frac{PV}{VRT+PRTB}*(
    
    
    
    
    \frac{R}{P}+
    
    
    
    
    \frac{d}{dT}
    
    
    
    
    \frac{RTB}{V})
    I need help with
    Code:
    
    
    
    
    
    \frac{d}{dT}
    
    
    
    
    \frac{RTB}{V})
    I dont know the latex format for pd
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by j-lee00 View Post
    I dont know the latex format for pd
    Basically the same thing that you have, except replace [tex] with [tex] and [/tex] with [/tex] .

    -Dan
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  3. #3
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    To use TeX here use [ MATH] and [ /MATH] without the spaces.

    Here is what you posted:


    PV = RT(1+B(T)/V)


    \beta = (1/V)*(\frac{dV}{dT})

    at constant P

    show

    \beta = \frac{1}{T}*\frac{V + B + T\frac{dB}{dT}}{V + 2B}

    I got to

    \beta=\frac{PV}{VRT+PRTB}*(\frac{R}{P}+\frac{d}{dT  }\frac{RTB}{V})

    I need help with

    \frac{d}{dT}\frac{RTB}{V}
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  4. #4
    Forum Admin topsquark's Avatar
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    I need help with

    \frac{d}{dT}\frac{RTB}{V}
    I haven't look at the rest of it, but since R and B are constant it would seem to be that
    \frac{d}{dT} \left ( \frac{RTB}{V} \right ) = \frac{RB}{V} - \frac{RTB}{V^2}~\frac{dV}{dT}

    -Dan
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  5. #5
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    B(T) not a constant
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by j-lee00 View Post
    B(T) not a constant
    Okay, then
    \frac{d}{dT} \frac{RTB}{V} = R \left ( \frac{B}{V} + \frac{T}{V} \frac{dB}{dT} - \frac{TB}{V^2}\frac{dV}{dT} \right )

    (This is a rather messy problem you've got here, isn't it?)

    -Dan
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