Introduction & Context

Resistance thermometers (RTDs) exploit the predictable change in electrical resistance of pure metals with temperature. The Pt100 sensor, constructed from platinum with a nominal resistance of 100 Ω at 0 °C, is the industrial standard for accurate and stable temperature measurement in process plants, refineries, power generation, food & beverage, and pharmaceutical facilities. A quick linear calculation converts the measured resistance into temperature, providing operators and control systems with a real-time value that is critical for safety, product quality, and energy efficiency.

Methodology & Formulas

Reference resistance
Let \( R_{0} \) be the sensor resistance at the ice point (0 °C).
Temperature coefficient
The IEC 60751 standard defines the linear temperature coefficient \( \alpha \) such that
\[ R(T) = R_{0}\left(1 + \alpha T\right) \] where \( T \) is the temperature in °C.
Resistance deviation
Compute the deviation of the measured resistance \( R_{\text{meas}} \) from the reference:
\[ \Delta R = R_{\text{meas}} - R_{0} \]
Temperature calculation
Rearranging the linear relation gives the calculated temperature:
\[ T_{\text{calc}} = \frac{\Delta R}{\alpha R_{0}} \]

The linear model is valid only within the following resistance bounds:

Limit	Resistance Condition
Lower	\( R_{\text{meas}} \geq R_{0}\left(1 + \alpha\,T_{\text{min}}\right) \)
Upper	\( R_{\text{meas}} \leq R_{0}\left(1 + \alpha\,T_{\text{max}}\right) \)

Use the Callendar–Van Dusen equation for the specific RTD type (typically α = 0.00385 Ω/Ω/°C).

Measure the resistance R_t at the sensor leads (after compensating for lead resistance if 3- or 4-wire configuration is used).
Calculate the temperature t from: t = (R_t – R₀) / (α · R₀) where R₀ = 100 Ω at 0 °C.
For higher accuracy (±0.01 °C) use the full Callendar–Van Dusen coefficients or the ITS-90 reference function supplied by the manufacturer.

It depends on wire gauge and allowable error. A practical rule for 24 AWG copper leads and a 100 Ω RTD is:

2-wire: keep leads shorter than 3 m for ±0.1 °C accuracy.
3-wire: up to 300 m is acceptable if the three conductors have matched resistance within ±0.1 Ω.
4-wire: theoretically unlimited; ensure excitation current is low enough (≤1 mA) to avoid self-heating.

Perform an in-situ resistance measurement and compare to the expected value at the known process temperature:

Record the stabilized process temperature from a calibrated reference (e.g., a secondary standard thermometer).
Measure the RTD resistance; convert to temperature using the same CVD coefficients used for calibration.
If the deviation exceeds the class tolerance (Class A ±0.15 + 0.002|t| °C, Class B ±0.3 + 0.005|t| °C), schedule replacement or recalibration.

Keep self-heating ≤25 % of the sensor’s specified tolerance:

For a 1/10 DIN RTD in moving water, 1 mA gives ≈0.01 °C rise; 2 mA gives ≈0.04 °C.
In still air, limit current to 0.5 mA to stay under 0.1 °C rise.
Use pulsed excitation (e.g., 100 ms on, 900 ms off) in low-power DCS cards to cut average power by 90 %.

Worked Example – Converting RTD Resistance to Temperature in a Reactor Loop

A process engineer is validating the temperature reading of a Pt100 RTD installed in the cooling-water return line of an exothermic reactor. The DCS shows a resistance value of 107.7 Ω and must confirm that the corresponding temperature is within the safe operating window.

Knowns

R₀ (ice-point resistance) = 100.0 Ω
α (temperature coefficient) = 0.00385 °C^-1
Measured resistance R_meas = 107.7 Ω
Valid RTD range: –200 °C to 650 °C

Step-by-step calculation

Compute the resistance change: \[ \Delta R = R_{\text{meas}} - R_0 = 107.7 - 100.0 = 7.7\ \Omega \]
Use the linear RTD approximation for temperatures near 0 °C: \[ T = \frac{\Delta R}{\alpha \cdot R_0} \]
Insert the numeric values: \[ T = \frac{7.7}{0.00385 \times 100.0} = \frac{7.7}{0.385} = 20.0\ °C \]

Final Answer

The Pt100 RTD indicates a process temperature of 20.0 °C, which lies within the allowable range and confirms the cooling loop is operating at the desired set-point.

"Un projet n'est jamais trop grand s'il est bien conçu." — André Citroën

"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise." — Charles de Gaulle