Simulating and Fitting Data for Chemical Reactions

[Csaba Tizedes]

(11-28-2019 01:05 PM)Namir Wrote:  Additional references, links, and equations are most welcome.

If you interested, my method for finding the limit of a solution of a 1st order ODE (what is the value of a function if time goes to infinity, time is the independent, temperature is the measured value).

Rough translation: What is the room temperature if I measure it with a very slow, but accurate thermometer? I was in a very warm, but constant temperature room and I measured the room temperature with my CASIO wristwatch at every ten (10) minutes. After the 3rd measurement (t=30 min) the thermometer reading not fixed, I continued the measurement, but I want to calculate the room temperature earlier than it fixed.

The temperature can be estimated with a well known exponential solution of 1st order ODE, but in this case the ambient temperature is not known.

The method: Let's calculate SD of the constant (k) in every measured point and minimize the relative error (=SD of k / average k) in the function of the ambient temperature.

The result on the second page (diagram).

As you can see, the minimum is very sharp, if we can measure the temperature +/-0.05°C (yes, the displayed temperature resolution is 0.1°C on the CASIO), the minimum of the function also can be found with similar accuracy.

The two little program written on a CASIO fx-50F for faster calculation. The used data was t=0...30min range.

Csaba