The lines or chart of Dühring are in fact a plot of the boiling temperature of a solution, with constant concentration, against the boiling temperature of a reference substance. All this at constant total pressure.
This is a key tool for evaporation process estimations since rather than requiring a large amount of experimental data for the evaporation of a solution, and then for different concentrations of it, you only need a few data points and a the, approximate, correlation proposed by Düring (which produces straight lines).
 |
| A sketch of a Duhrings line plot |
You should be aware that, strictly speaking, not all Dühring lines are (or should be) parallel nor straight lines.
CONTENTS
1.1 Dühring's plot for BrNa solutions
1 Plotting Dühring lines
To be honest, the chart or lines of Dühring are actually useless since using graphical methods to estimate data would introduce error or increase it into the evaporator or the like calculations. A more realiable method would be to get any unknown data directly from the few experimental available data (which would have been also used for the generation of the Dühring's chart).
Anyway, here we shall present the method for the generation of a Dühring's chart and later an automated and more precise way of calculation.
First, the pressures for the reference substance to be considered are those corresponding to vapor pressure. Also, it is common that the reference substance is: water. The reason why water is commonly used as reference substance is because of its universal solvent properties. Therefore, vapor pressure data for water is required.
You may get some vapor data in the following excel file or make a copy of the following Google Sheets file.
The first Dühring line should be easy to draw since it corresponds to 0% concentration. Since the reference fluid (water in this case) is exactly the same as the solution (with 0% concentration) in the Dühring's plot we should get a straight line at exactly 45$^\circ$.
In order to draw futher Dühring lines, temperature and pressure data for the solution are required. This temperature would be used as the ordinate of a point whose abscissa is the boiling temperature of water which should be retrieved from the steam table (see above) at the initially given pressure.
In this way, only a few data is needed to draw a straight line as a reasonable estimation of missing information.
1.1 Dühring's plot for BrNa solutions
Consider the following data for vapor pressure at different temperatures for BrNa solutions and then draw a Dühring's plot.
| Solution concentration |
Vapor pressure in mm Hg | ||
|---|---|---|---|
| At 10 C | At 50 C | at 80 C | |
| 0 % | 9.21 | 93.54 | 355.47 |
| 10 % | 8.9 | 89.7 | 344.5 |
| 40 % | 7.8 | 77.8 | 299 |
| 60 % | 6.9 | 69.1 | 265.5 |
With the data provided in the table above at least 4 Dühring lines can be drawn, one already known as it corresponds to 0% concentration. In order to make things easy, the following tables for 0%, 10% and 40% were prepared,
 |
| Data points for plotting Dühring lines for 0%, 10% and 40% concentration. Points to be plot are in the last two columns. |
Data for the 60% concentration is left for the reader to calculate. As was promised, all this data leads to straight, or almost, lines. The image below shows these lines.
Notice that in the plot above, the x and y axis are exchanged.
Please, access the following document to check out the Google Sheets file used to create the plot above.
1.2 Automated temperature estimation from Dühring's plot
Nowadays, several computational tools such as Excel, Google Sheets and even artificial intelligence are available to everyone. Therefore, using a print of the plot of Dühring lines would be obsolete and a waste of time.
In this section the idea of automated temperature (or pressure) estimation, in the evaporation process, is just depicted and it is left to the reader its implementation in the software of his/her preference.
If you are a user of a spreadsheets software, one way of doing this type of estimations is as follows,
- you would need the steam table data in the same file were you are to perform the pressure or temperature estimations,
- at least two points of vapor pressure and boiling tempearture at the same concentration for a working solution are required,
- if the vapor pressure is unknown for a known boiling temperature of the solution you need to search for a water boiling temperature related to a water vapor pressure that would be, according to Dühring's ideas, a good estimation of the solution vapor pressure,
- you may readily calculate the water boiling temperature from the equation of the straight line for the known Dühring line,
- once the water boiling temperature is known you should use this piece of information to estimate the corresponding water vapor pressure,
- the vapor pressure is calculated from the steam table. For this, you will, probably, need to perform a linear interpolation between two points in the steam table,
- the calculated water vapor pressure is the estimation of the solution vapor pressure you were looking for.
2 What you know about the lines of Dühring
Please, follow the link below to answer a small quizz and chek your knowledge on the topic presented in this post,
This is the end. I hope you will find this post useful.
Other stuff of interest
- LE01 - AC and DC voltage measurement and continuity test
- The pros and cons of bulb thermometers
- The pros and cons of bimetallic thermometers
- Some examples of temperature instruments
- Minor losses - Formulas
- What is a process variable?
- What are the most important process variables?
- Time dependence of process variables
- A list of process variables
- PID controllers for temperature
- Valves - Gate design
Ildebrando.
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