Determination of the mathematical model of the trial

In this step two we will define the mathematical model of the essay. The ISO 4787 guide details two calculation methods to obtain the volume contained in a volumetric flask. The first one indicates the calculation of the volume integrating all the magnitudes participating in the model into the equation. For a test, particularly for a defined temperature, a defined building material (glass), etc. Many of these values, such as water density and coefficient of expansion, can be considered constant, so this standard also proposes a tabulated factor to simplify the calculation. In this case we will use the complete equation to study the variables and their associated uncertainty. The equation (test model) will be:

The equation editor of MCM Alchimia is an ASCII editor that does not have special characters for which the Greek letters will have to be replaced by a common variable name. The main equation that will be put in Set equations will be V20 = ((Ml-Mv) / (Dens_w-Dens_a)) * (1- (Dens_a / Dens_b)) * (1-CDT * (t-20) ) where:

V20: Volume of the flask at 20ºC.
Ml: Mass (read on the scale) of the flask flush with detilated water (g).
Mv: Mass (read on the scale) of the empty flask (g).
Dens_w: Density of the water used in the calibration (g/ml).
Dens_a: Air density (g/ml).
Dens_b: Density of the masses with which the scale has been adjusted (g/ml).
CDT: Coefficient of cubic thermal expansion of the flask material (in 1/ºC).
t: Test water temperature (ºC).

It is advisable to make a deeper analysis of the sources of uncertainty of the input quantities of the model. In this way, if any magnitude has more than one source of uncertainty, it will be broken down into a sum of as many variables as there are sources of uncertainty, one of them will take the value of the magnitude and the rest will have zero value since they are added only for the purpose of evaluation of uncertainties.

More help

• First project – Step 1
• First project – Step 2-A: Basic model
• First project – Step 2-B: Input uncertainties
• First project – Step 2-C: Final model
• First project – Step 3.
• First project – Results.

Several estimations of uncertainty made with MCM Alchimia for advanced models of tests, calibrations or analytical techniques, can be consulted in several published scientific works, both by the software developer, as well as by other researchers in various branches of science. However, for a first contact with the application, in this document we will make a first simple calculation project to know the operation and the possibilities of the application. As an example, we will perform the calculations relevant to the calibration process of a calibration calibrated by the gravimetric method, consistent with the guide ISO 4787: 2010 Laboratory glassware – Volumetric glassware – Methods for use and testing of capacity

• Run the application from the desktop. Estra will already open in step 1.
• We write in the field Title : Calibration of a volumetric flask according to ISO 4787: 2010
• In the field Technical data we replace the pre-existing text with the technical description of our essay. There we can write the following text:
  This project consists of the evaluation of the calibration uncertainty of a 100 ml volumetric flask by the gravimetric method with ISO 4787: 2010. For this, a calibrated 1 mg division scale is available, with its calibration certificate, which tells us that if we assign the maximum correction of the reading in the working range to the uncertainty, it results in an expanded uncertainty of 0.0054 g for k (coverage factor) = 2.
  We also have a mercury glass thermometer of 0.01ºC, which also has a calibration certificate that indicates that at 20.00ºC it has an error of -0.022ºC and an expanded uncertainty of 0.012ºC for k = 2.
  The flask will be completely dried in an oven, cooled to 20°C, filled with distilled water and then weighed on the scale. This operation will be performed 5 times, taking the 5 mass values. To the average of these 5 mass values ​​and the temperature of the water filling, the equations of the standard will be applied to convert the mass value in Volume contained by the flask to 20ºC
• Having entered this data we can continue to the next step. By clicking on the link or the Step 2 button.

More help

• First project – Step 1
• First project – Step 2-A: Basic model
• First project – Step 2-B: Input uncertainties
• First project – Step 2-C: Final model
• First project – Step 3.
• First project – Results.