Your first Pt100 experiment

Make a Pt100 do something before you even own one.

In this experiment, Python will be our virtual temperature lab. We will change the temperature of an ideal Pt100, watch its resistance change, and then run the calculation backward as if we had measured a real sensor.

• Hardware: none
• Time: about 10–15 minutes
• You need: Python 3.11+ and rtd-sensor

If you have not installed the package yet, start with the RTD Playground introduction.

The question

A Pt100 is a temperature sensor, but what does it actually measure?

More specifically:

What happens to the electrical resistance of a Pt100 when its temperature changes?

We can answer that with just a few lines of Python.

Two facts before we begin

RTD stands for resistance temperature detector. Its electrical resistance changes in a predictable way as its temperature changes.

The name Pt100 gives us two useful clues:

• Pt means the sensing element is platinum.
• 100 means an ideal Pt100 has a resistance of 100 ohms at 0 °C.

Experiment 1: discover the "100" in Pt100

Start at 0 °C:

from rtd_sensor import pt100

resistance = pt100.celsius_to_resistance(0.0)
print(f"At 0 °C: {resistance:.4f} ohms")

You should see:

At 0 °C: 100.0000 ohms

So the 100 in Pt100 is not just a model number. At 0 °C, the ideal standardized sensor really is 100 ohms.

Experiment 2: warm up the virtual sensor

Before running the next example, make a prediction.

Now change the temperature:

from rtd_sensor import pt100

resistance = pt100.celsius_to_resistance(20.0)
print(f"At 20 °C: {resistance:.4f} ohms")

The result is:

At 20 °C: 107.7935 ohms

The temperature went up, and so did the resistance.

Try 25 °C:

resistance = pt100.celsius_to_resistance(25.0)
print(f"At 25 °C: {resistance:.4f} ohms")

At 25 °C: 109.7347 ohms

That gives us our first useful rule of thumb:

For a Pt100, resistance increases as temperature increases.

Experiment 3: make a resistance table

One value at a time does not show us much of a pattern. Let's ask for several values:

from rtd_sensor import pt100

for temperature_c in [0, 10, 20, 30, 40, 50, 100]:
    resistance = pt100.celsius_to_resistance(temperature_c)
    print(f"{temperature_c:>3} °C  ->  {resistance:.4f} ohms")

You should get:

  0 °C  ->  100.0000 ohms
 10 °C  ->  103.9025 ohms
 20 °C  ->  107.7935 ohms
 30 °C  ->  111.6729 ohms
 40 °C  ->  115.5408 ohms
 50 °C  ->  119.3971 ohms
100 °C  ->  138.5055 ohms

What happened?

Three things should stand out:

1. At 0 °C, the ideal Pt100 is 100 ohms.
2. Resistance rises as temperature rises.
3. A 10 °C temperature change changes the resistance by only a few ohms.

Now look more closely at the 10-degree steps. Does the resistance increase by exactly the same amount every time?

It is close, but not quite.

That small clue will matter in a later experiment when we ask whether a Pt100 is really linear.

Experiment 4: pretend we measured a real Pt100

So far we have started with temperature and asked for resistance:

temperature  ->  resistance

A real thermometer usually needs to do the opposite. Hardware measures the sensor's resistance, and we need to determine the temperature:

measured resistance  ->  temperature

Imagine that some measurement hardware reports a Pt100 resistance of 119.3971 ohms.

Ask rtd-sensor what temperature that represents:

from rtd_sensor import pt100

measured_resistance = 119.3971
temperature_c = pt100.resistance_to_celsius(measured_resistance)

print(f"Measured resistance: {measured_resistance:.4f} ohms")
print(f"Temperature: {temperature_c:.2f} °C")

You should see:

Measured resistance: 119.3971 ohms
Temperature: 50.00 °C

That is the basic job rtd-sensor will eventually perform with a physical sensor: take the best available estimate of the Pt100's resistance and convert it to temperature.

Try your own experiments

Do not stop with the values above. Change something and see what happens.

• What resistance does a Pt100 have at 37 °C?
• What about -20 °C?
• Change the temperature from 20 °C to 21 °C. How much does the resistance change?
• Pick a temperature of your own, calculate its resistance, then feed that resistance into pt100.resistance_to_celsius(). Do you get back where you started?
• Try this mystery resistance: 114.3817 ohms. What temperature is it close to?

What changes when the Pt100 is real?

Our values so far came from the ideal standardized Pt100 curve. A physical measurement introduces more questions:

• Is the real probe exactly on the ideal curve?
• How accurately did we measure its resistance?
• Did the wires add resistance of their own?
• Is the probe actually at the same temperature as the thing we are trying to measure?

We do not need to solve those problems yet. For now, the important thing is that the resistance-to-temperature relationship itself makes sense.

Later experiments will add those real-world effects one at a time.

What you learned

You have now made your first virtual Pt100 measurement and discovered that:

• a Pt100 is a platinum resistance temperature detector;
• an ideal Pt100 is 100 ohms at 0 °C;
• its resistance increases as temperature increases;
• the relationship is close to linear over ordinary ranges, but not exactly;
• rtd-sensor can calculate temperature → resistance;
• rtd-sensor can also calculate resistance → temperature;
• real measurement hardware and the RTD model have different jobs.

And you did all of it without owning a sensor.

Next experiment

A table hints at the shape of the Pt100 relationship. A graph makes it much easier to see.

Next: Plot an RTD curve and see what the Pt100 looks like from -200 °C to 850 °C.