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Math Help - Determination of constants

  1. #1
    jturn14
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    Determination of constants

    Hi, i'm having this problem with an engineering formula I have to do something with.

    First, let me explain what it is. the experiment is to experimentally determine the latent heat of vaporization for water between 50 C and 100 C in a depressurized vapor (so only the vapor pressure affects it). part of the analysis is to find constant relating the heat of vaporization (h(fg)) to the temperature.

    To do this, I use an integrated form of the clapeyron equation with h(fg) represented as A+BT, where T is temperature and A and B are the constants. Also, I use a linear regression giving ln(P) = f(T), (the integrated form of the Clapeyron equation.

    Basically, what I have is this:

    ln(P) = (1/R)*(B*ln(T) - (A/T)), where R is the universal gas constant, P is the pressure, T is the temperature, and A and B are the constants in question.

    Also, i have, from the regression, ln(P) =0.0403*T - 10.414. I can also do a logarithmic regression, giving me ln(P) = 14.032*ln(T) -78.508. Somehow, I need to use these two (or one of these) equations to find A and B in terms of R, P, and T.

    Any help would be GREAT (the TA wasn't very useful).
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by jturn14 View Post
    Hi, i'm having this problem with an engineering formula I have to do something with.

    First, let me explain what it is. the experiment is to experimentally determine the latent heat of vaporization for water between 50 C and 100 C in a depressurized vapor (so only the vapor pressure affects it). part of the analysis is to find constant relating the heat of vaporization (h(fg)) to the temperature.

    To do this, I use an integrated form of the clapeyron equation with h(fg) represented as A+BT, where T is temperature and A and B are the constants. Also, I use a linear regression giving ln(P) = f(T), (the integrated form of the Clapeyron equation.

    Basically, what I have is this:

    ln(P) = (1/R)*(B*ln(T) - (A/T)), where R is the universal gas constant, P is the pressure, T is the temperature, and A and B are the constants in question.

    Also, i have, from the regression, ln(P) =0.0403*T - 10.414. I can also do a logarithmic regression, giving me ln(P) = 14.032*ln(T) -78.508. Somehow, I need to use these two (or one of these) equations to find A and B in terms of R, P, and T.

    Any help would be GREAT (the TA wasn't very useful).
    Using your ln-ln regression and comparing coefficients with the Clapeyron equation:
    \frac{1}{R}B = 14.032
    -\frac{1}{R} \frac{A}{T} = -78.508 (For some specific T. See below.)

    You know the value for R, so you can get B from the first equation. For the second part, what is your intercept value for T? That is at what temperature T on the ln-ln plot is ln(P) = -78.508? It's T = 1 of course. So the second equation will read:
    -\frac{1}{R} \frac{A}{1} = -78.508

    You can now use this to find A.

    -Dan
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