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Error propagation of q=mcdeltat

  1. Dec 12, 2012 #1
    1. The problem statement, all variables and given/known data
    I want to know how to do error propagation on this

    cNi= [-(mcΔt)Al-(mcΔt)H2O]/(mΔt)Ni

    m is mass and Δt is change in temperature

    2. Relevant equations

    δc/c=√(δm/m)2+(δ(Δt)/Δt)2

    3. The attempt at a solution

    I know the above error prop eq. above applies to c=Q/mΔt
    or I think it does.

    But I just cant figure it out. The uncertainty for both is about 0.1. I have about 3 different values mass and 2 different values for temperature. What values do I substitute into the error prop equation. Any help would be great. Doing it last minute and its becoming a nightmare.
     
  2. jcsd
  3. Dec 12, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    When you're looking to propagate the errors when the solution is a non-trivial function of several variables, I'd suggest using the partial derivative method. This avoids breaking the function down into elementary additions, multiplications, powers, etc., and slogging through the error math for each one of them.

    If you have a function of, say, three variables f(x,y,z), and associated uncertainties Δx, Δy, Δz, for the variables, then the uncertainty in the result of a calculation of f(x,y,z) is given by:

    $$Δf = \sqrt{\left(\frac{\partial f}{\partial x}\right)^2 Δx^2 + \left(\frac{\partial f}{\partial y}\right)^2 Δy^2 + \left(\frac{\partial f}{\partial z}\right)^2 Δz^2} $$

    This is easy to remember, applies to function of any number of variables, and best of all it always works, even if the function f contains other functions like sin(x) or ln(x) or,...
     
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