Calculating tau from measured time and temperature

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SUMMARY

This discussion focuses on calculating the tau value from two data points using the exponential decay model defined by the equation f(t) = Tf(1 - exp(-t/Tau)). The provided data points are T1 = 64.68 at t1 = 200.7 and T2 = 84.15 at t2 = 243. The user attempted to solve the equations simultaneously but encountered difficulties simplifying the exponential terms. Ultimately, a numerical evaluation approach was suggested, leading to a calculated tau value of -327.156 and Tf of -76.3792.

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blairj
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so i have two data points. T1 = 64.68, t1 = 200.7 and T2 = 84.15, t2 = 243. I want to use this data to find the tau value of the exponential curve the data came from.

I was trying to use simultaneous equations but got stuck. Can anyone help me with this?

64.68 = Tf(1-exp(-200.7/Tau))
84.15 = Tf(1-exp(-243/Tau))

I got to 19.47 = 84.15*(exp-200.7/Tau) - 64.68*(exp-243/Tau)

I want to get a value for Tau but i can't figure out how to simplify/remove the exponential terms.
Any help is appreciated
 
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What are you trying to fit? A function of the form

[tex]f(t) = T_f(1 - exp(\frac{-t}{\tau}))[/tex]

Your best bet it to evaluate it numerically, don't think it can be analytically solved...

I get tau = -327.156 and Tf = -76.3792
 
Last edited:

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