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Math Help - How to solve for unknowns ?

  1. #1
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    How to solve for unknowns ?

    Here is the question , i tried to solve it using lns but didnt work out for me

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  2. #2
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    Quote Originally Posted by kaboose786 View Post
    Here is the question , i tried to solve it using lns but didnt work out for me

    Z = aV^bP^c, take the \ln from both side,..

    \ln Z = \ln a + b \ln V + c \ln P

    for P constant, we have

    \ln Z_{2} = \ln a + b \ln V_{2} + c \ln P . . .eqn (1)

    \ln Z_{3} = \ln a + b \ln V_{3} + c \ln P . . .eqn (2)


    from eqn (1) - eqn (2), we have

    \ln Z_{2} - \ln Z_{3}= b ( \ln V_{1} - \ln V_{2})
    solve it.

    for V constant,. use the same method to find c.

    once you find b and c,..you'll get a.
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  3. #3
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    \ln(z) = \ln(a)+b\ln(V)+c\ln(P)

    so, using the data obtained from the three trials, you'll get three equations in a, b, c, which you can then solve by using Cramer's rule, Matrix method, or using a calculator.


    2) Obviously the most accurate would be Linear Regression, (I think) but there is another method I can spot here.

    For trials 1,2,3 and 4, the Pressure remains constant. Therefore, you can assume the the above equation as being only a function of volume.

    So plot a graph of the 4 readings Vs ln(V) \ln(z) = \ln(a)+b\ln(V) + c\ln(11.2)

    The slope of this graph gives you the value of b.


    Now for trials 5,6,7 observe that the volume remains constant, hence plot the graph of \ln(z) = \ln(a)+ c\ln(P) + b\ln(V)

    The slope of this graph would give you the value of c.

    Now using c, and b obtained thus, you can estimate a.
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  4. #4
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    Quote Originally Posted by dedust View Post
    Z = aV^bP^c, take the \ln from both side,..

    \ln Z = \ln a + b \ln V + c \ln P

    for P constant, we have

    \ln Z_{2} = \ln a + b \ln V_{2} + c \ln P . . .eqn (1)

    \ln Z_{3} = \ln a + b \ln V_{3} + c \ln P . . .eqn (2)


    from eqn (1) - eqn (2), we have

    \ln Z_{2} - \ln Z_{3}= b ( \ln V_{1} - \ln V_{2})
    solve it.

    for V constant,. use the same method to find c.

    once you find b and c,..you'll get a.
    thanks a lot for replying am done part a with ur help .. appreciated
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