Calculating tau from measured time and temperature

In summary, the conversation revolved around using two data points with corresponding temperatures and times to find the tau value for an exponential curve. The person encountered difficulties when trying to use simultaneous equations and was seeking help to simplify and solve for the desired tau value. Another person suggested evaluating the function numerically instead of analytically, and provided their own numerical values for tau and Tf.
  • #1
blairj
1
0
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
 
Physics news on Phys.org
  • #2
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:

1. What is tau and why is it important in scientific calculations?

Tau (τ) is a mathematical constant that represents the time constant in an exponential decay or growth function. It is important in scientific calculations because it allows us to model and predict the behavior of systems that exhibit exponential decay or growth, such as radioactive decay or chemical reactions.

2. How do you calculate tau from measured time and temperature?

The calculation of tau (τ) from measured time and temperature involves using the Arrhenius equation, which relates the rate of a reaction or process to the temperature at which it occurs. The equation is τ = (k * T) / (Ea * R), where k is the rate constant, T is the temperature in Kelvin, Ea is the activation energy, and R is the gas constant. By plugging in the values for these variables, you can solve for tau.

3. Can tau be used in other types of calculations besides exponential decay or growth?

Yes, tau can also be used in other types of calculations such as calculating the time constant for a capacitor in an RC circuit, or the time constant for an inductor in an RL circuit. It can also be used in pharmacokinetics to calculate the elimination rate constant for a drug from its half-life.

4. How do you interpret the value of tau in a scientific calculation?

The value of tau (τ) represents the time it takes for a system to reach 63.2% of its final value in an exponential decay or growth function. It is also known as the time constant, and a larger value of tau indicates a slower rate of decay or growth, while a smaller value indicates a faster rate. In general, the smaller the value of tau, the more rapid the change in the system.

5. Are there any limitations to using tau in scientific calculations?

One limitation of using tau (τ) in scientific calculations is that it assumes a constant rate of decay or growth, which may not always be the case in real-world systems. Additionally, the calculation of tau relies on accurate and precise measurements of time and temperature, so any errors in these measurements can affect the accuracy of the result. It is important to consider these limitations when using tau in scientific calculations.

Similar threads

A Convergence of an infinite series of exponentials
    • Calculus
Replies
6
Views
2K
Derivation from simultaneous equations (Fabry-Perot etalon)
    • Precalculus Mathematics Homework Help
Replies
11
Views
2K
I Understanding 2 equivalent formulations of both data set measures
    • Set Theory, Logic, Probability, Statistics
Replies
9
Views
1K
Which threshold value provides the most accurate results for muon decay time?
    • Advanced Physics Homework Help
Replies
16
Views
2K
I Warm-up time for a hollow cylinder
    • Thermodynamics
Replies
5
Views
1K
Engineering Calculating the mass of air in a pressurised air tank
    • Engineering and Comp Sci Homework Help
Replies
14
Views
1K
Calculating time to reduce alcohol in wine using heating method
    • Chemistry
4
Replies
131
Views
4K
Exponential integral over removeable singularity gives wrong result
    • Calculus
Replies
3
Views
2K
B What is the true way to determine time parameters from semilog graph?
    • Other Physics Topics
Replies
2
Views
8K
I Calculation of temperature changes (heating a cube in a microwave oven)
    • Thermodynamics
Replies
9
Views
708

Hot Threads

Recent Insights

Back
Top