RTD Self-Heating in Air vs Liquid: The Coefficient Matters

RTD self-heating depends on both electrical power and how effectively the installed sensor transfers that heat to its surroundings. The same excitation current can produce a larger temperature rise in air than in liquid, but neither medium has a universal coefficient. Use a coefficient specified for the sensor construction and relevant test conditions—not a default selected only because the application involves “air” or “liquid.” IST AG’s manufacturer data show different coefficients for different element sizes and media.

A Pt100 carrying 1 mA does not always dissipate 0.14 mW. At 0 °C, its nominal resistance is 100 Ω, so the power is 0.100 mW. For a nominal 3850 ppm/K Pt100 at 100 °C, the power is approximately 0.139 mW. Temperature, resistance, and current must therefore be stated together.

Calculate Power Before Temperature Rise

For steady DC excitation, electrical power dissipated in the sensing element is:

[
P=\frac{I^2R}{1000}
]

where:

• (P) is sensing-element power in mW.
• (I) is current through the element in mA.
• (R) is element resistance at the operating temperature in Ω, excluding external lead resistance.

This is the mA-based equivalent of the self-heating relationship in IST AG’s RTD Platinum Sensor application note, revision ATP_E2.4.4, Section 8.

Correcting the Pt100 Power Example

For the 3850 ppm/K characteristic, the same application note gives the following nominal resistance relationship over 0–850 °C:

[
R(T)=100\left(1+3.9083\times10^{-3}T-5.775\times10^{-7}T^2\right)
]

Here, (T) is temperature in °C and (R(T)) is resistance in Ω. This characteristic must match the actual RTD; it is not interchangeable with every platinum sensor curve.

At 1.00 mA:

Resistance is rounded to three decimal places and power to four. These are nominal calculations, not measured sensor results.

For a small self-heating rise, resistance at the medium temperature is a practical first approximation. If the predicted rise is substantial, resistance also changes as the element warms, and a constant-resistance estimate needs further evaluation.

Check the Coefficient Units

The units determine whether to multiply or divide.

Self-Heating Coefficient: K/mW

When the coefficient describes temperature rise per unit power:

[
\Delta T=SP
]

where (S) is the self-heating coefficient in K/mW and (\Delta T) is temperature rise in K. A temperature rise of 1 K is numerically equal to a rise of 1 °C. IST AG uses this coefficient convention in its application note.

Dissipation Constant: mW/K

When a datasheet instead gives power dissipated per unit temperature rise:

[
\Delta T=\frac{P}{D}
]

where (D) is the dissipation constant in mW/K.

For the same sensor under the same conditions, (D=1/S). A larger K/mW value means more self-heating; a larger mW/K value means less. Do not transfer a number between these conventions without taking its reciprocal.

Air vs Liquid: A Manufacturer-Based Example

IST AG’s application note, Section 9, lists these self-heating coefficients for its chip-size designation 202:

The table’s reference condition is a Pt100 at 0 °C with 1 mA excitation. Its self-heating columns have different conditions from some adjacent response-time columns, so read the column headings carefully.

Using (P=0.100) mW:

[
\Delta T_{\text{ice water}}=0.031\times0.100
=0.0031\ \text{K}
]

[
\Delta T_{\text{air}}=0.313\times0.100
=0.0313\ \text{K}
]

These correspond to 3.1 mK and approximately 31 mK, consistent with the manufacturer’s rounded reference values. Under these particular conditions, the air result is about ten times larger. This does not establish a universal air-to-liquid ratio or a coefficient for still air.

Nor does it justify universal defaults such as 0.05 K/mW for liquid or 0.1–0.5 K/mW for air. The manufacturer’s table varies with element size, and its application note warns that assembly and measurement conditions can change self-heating. Element data alone do not establish the coefficient of a completed sheathed or thermowell-mounted assembly.

Check the Installation Before Using the Result

Before estimating self-heating:

1. Identify the actual RTD element or probe assembly and its resistance characteristic.
2. Obtain the excitation current from the connected instrument’s documentation or configuration.
3. Confirm the coefficient’s units, test temperature, medium, flow velocity, and whether it describes a bare element or complete probe.
4. Check whether immersion, mounting, and thermal contact are sufficiently comparable to the stated test conditions.
5. If no representative coefficient is available, treat the temperature rise as undetermined rather than assigning a generic medium-based value.

Reducing current reduces power quadratically: at unchanged resistance, reducing excitation from 1 mA to 0.5 mA reduces power—and the constant-coefficient estimate of temperature rise—to one quarter. However, the lower current must remain compatible with the readout’s measurement requirements. IST AG recommends minimizing excitation to reduce self-heating while considering the required measurement performance.

An estimated self-heating rise is one contribution to measurement error, not total measurement uncertainty or a calibration verdict. Compare it with the application’s allocated error budget using the applicable procedure and decision rule. A plausible calculation alone cannot establish that an installed temperature loop passes calibration.