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Math Help - please! tricky logs (i think!) question.

  1. #1
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    please! tricky logs (i think!) question.

    hiya

    this is a really horrible q i'd dearly love some advice for.
    Q: Gas expands in a space according to a law "P=CV^n"
    P is pressure kNm^-2, V is volume m^3, C and n are constants.
    an experiment produces these results
    P: 100 | 200 | 300 | 400 | 500
    V: 0.165 | 0.104 | 0.079 | 0.064 | 0.055
    a) explain carefully how you would plot a graph to verify P and V follow a relationship according to the above law; what would be plotted on each axis?
    b)supposing a straight line on the graph passes through the first and last data points, find the values of C and n in this example. there is no need to plot an accurate graph here.

    I really just need some pointers on how to go about this as I'm utterly flummoxed!!
    thanks so so much!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by synnr View Post
    hiya

    this is a really horrible q i'd dearly love some advice for.
    Q: Gas expands in a space according to a law "P=CV^n"
    P is pressure kNm^-2, V is volume m^3, C and n are constants.
    an experiment produces these results
    P: 100 | 200 | 300 | 400 | 500
    V: 0.165 | 0.104 | 0.079 | 0.064 | 0.055
    a) explain carefully how you would plot a graph to verify P and V follow a relationship according to the above law; what would be plotted on each axis?
    plot the P on the y-axis and the V on the x-axis.

    b)supposing a straight line on the graph passes through the first and last data points, find the values of C and n in this example. there is no need to plot an accurate graph here.
    for the first point, you have P = 100, and V = 0.165, thus you have the relationship: 100 = C(0.165)^n

    for the last point, you have P = 500 and V = 0.055, thus you have the relationship: 500 = C(0.055)^n

    thus you need to solve the system:

    100 = C(0.165)^n .........................(1)
    500 = C(0.055)^n ..........................(2)

    for C and n

    incidentally, this is probably how I'd deduce that the relationship works in part (1), solve for C and n between each pair of points, but that may be too tedious. you may be able to tell what, say n is by the shape of the graph. if it is like a parabola, you know n = 2, for example
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