## Temperature compensation in conductivity measurement

In an earlier article, we talked about temperature, and I said I could give a very scientific explanation of it. Well, the time has come. Here we’ll use the kinetic theory approach to explain temperature so you can understand how conductivity depends on it.

### Temperature x conductivity

On a microscopic level, physical bodies consist of a combination of molecules and particles. Particles have a degree of freedom, which determines their kinetic energy. The average kinetic energy of these particles makes what we know as a body’s temperature.

Free moving particles – does that ring a bell? When we talked about conductivity sensors, we mentioned free ions, right? So, if conductivity and temperature depend on the rate of particle movement in a medium, then you can get an idea about how they relate.

Raising the temperature of the medium increases the movement of its particles, including its free ions, thus raising its conductivity.

This means that even a small change in temperature can affect the conductivity of a liquid. To avoid measurement changes for every slight change in temperature, transmitters show a compensated reference reading (typically at 25 degrees Celsius) instead of the real raw value.

### The compensation

Now that we know why we compensate, let’s learn two ways to do it.

You can do a linear compensation if your process temp doesn’t vary much. But if you have bigger variations, then you should use a compensation table. Let’s see how to do each, and you can decide which fits your needs better.

#### Linear compensation

The relationship between temperature and conductivity depends on factors such as composition and concentration. To determine this relationship, we calculate the coefficient alpha (α). Alpha represents how much a liquid’s conductivity changes, in percentages, if the temperature increases 1 Kelvin.

When your solution stabilizes at a certain temperature, write down the temperature and conductivity and use this formula to find your α.

Now this method assumes that the coefficient has the same value for all temperatures, which is not true. However, if you only have a small variation on your temperature range, this should result in a minimal effect on the overall error margin.

#### Non-linear compensation

For a bigger temperature range, linear compensation might not give accurate readings throughout the range. The relationship between temperature and conductivity might change for different temperatures or solutions.

For liquids with up to five percent of dissolved salts, for example, the alpha increases with temperature increases. And the α for natural water decreases when the temperature  increases.

So how do we compensate in these cases? With the good old empirical table, measuring the conductivity for each increment inside the temperature range.

To do this, you must take a series of conductivity measurements of your process liquid sample at various temperatures and calculate the alpha for each. After you have all the data in a table, you can feed this table to your transmitter for more accurate readings.

#### Automatic temperature compensation (ATC)

Many sensors in the market come with automatic temperature compensation (ATC), which basically boils down to a few tables for known solutions.

Common non-linear ATC methods for conductivity sensors:

• Sodium chloride (IEC 746-3) for solutions with up to five percent of dissolved salts
• Water (ISO 7888) for natural water, usually between 100 and 1000 micro-Siemens per centimeter
• Ultrapure sodium chloride water for water treated for high purity, if including pH-neutral impurities
• Ultrapure hydrogen chloride for water treated for high purity, having passed a cation exchanger (also suitable for ammonia and caustic soda)
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