Temperature Measurement: RTD, Thermocouple, Thermistor & IR

Temperature is the most measured variable in industry. Learn RTDs (Pt100, Callendar–Van Dusen, 2/3/4-wire), thermocouples (Seebeck effect, types, cold-junction compensation, extension wires), thermistors, semiconductor sensors, infrared pyrometers and emissivity, thermowells and response time — with Python for Pt100 conversion, lead-wire error and CJC.

Almost every process is sensitive to temperature: reaction rates, viscosity, product quality, safety limits. Industrial plants have thousands of temperature points, most measured by RTDs (accurate, −200 to 600 °C) or thermocouples (rugged, up to 1700 °C+).

Choosing and installing the sensor correctly matters as much as the sensor itself: lead-wire resistance, cold-junction compensation and thermowell design are the classic sources of error.

An analogy

An RTD is a thermometer that reports by changing its resistance, like a road that gets 'longer' when hot; a thermocouple is a tiny battery whose voltage depends on the temperature difference between its two ends — so you must always know the temperature of the 'cold' end.

RTDs

A platinum wire or film whose resistance rises almost linearly with temperature: Pt100 = 100 Ω at 0 °C, 138.51 Ω at 100 °C. Accuracy classes AA/A/B (IEC 60751) define tolerance, e.g. class A ±(0.15 + 0.002|T|) °C. They are stable and accurate but need excitation current and are slower and more fragile than thermocouples.

Thermocouples

Two dissimilar metals joined at the hot end produce a small voltage (Seebeck effect) proportional to the temperature difference between hot and reference (cold) junctions. Common types: J (iron–constantan, to 750 °C), K (chromel–alumel, to 1250 °C), T (copper–constantan, cryogenic), N, and noble-metal R, S, B (to 1700 °C). They are cheap, fast and rugged but less accurate (±1–2 °C) and need cold-junction compensation and matching extension wires.

Other sensors

Choose by range, accuracy and cost:

Wiring and compensation

2-wire RTDs include lead resistance in the reading; 3-wire connections put leads in opposite bridge arms so they cancel (if equal); 4-wire uses separate current and sense leads and removes them entirely. Thermocouples need extension or compensating cable of the same type all the way to the transmitter, where an internal sensor measures the terminal temperature for CJC.

Installation: thermowells and response

Thermowells protect sensors from pressure and corrosion but add thermal lag and stem conduction error. Insertion length should be ≥ 10× the tip diameter to avoid conduction error, yet short enough to survive vortex-induced vibration — checked by the ASME PTC 19.3 TW-2016 wake-frequency calculation. Spring-loaded sensors and thermal paste improve response. Head-mounted transmitters convert to 4–20 mA/HART close to the sensor, reducing noise.

Formulas

Worked example: Pt100 reading

Given: Measured 138.51 Ω

Find: Temperature.

Answer: 100.0 °C

Worked example: Lead error

Given: 2-wire Pt100, 2 Ω total lead resistance

Find: Error.

Answer: ≈ +5.1 °C

Worked example: Cold-junction compensation

Given: Type K 3.075 mV, terminals at 25 °C, S = 41 µV/°C

Find: Hot-junction temperature.

Answer: ≈ 100 °C

Pt100 conversion, lead-wire error and thermocouple CJC

import math
# Pt100 (Callendar-Van Dusen, T >= 0 C) and type-K thermocouple (linear approx)
A, B, R0 = 3.9083e-3, -5.775e-7, 100.0
def pt100(T):
    return R0 * (1 + A * T + B * T * T)
def pt100_inverse(R):
    return (-A + math.sqrt(A * A - 4 * B * (1 - R / R0))) / (2 * B)
for T in (0, 100, 200):
    print(f"Pt100 at {T:3d} C = {pt100(T):.2f} ohm")
print(f"138.51 ohm -> {pt100_inverse(138.51):.2f} C")

# 2-wire lead error: 2 x 5 m of 0.2 ohm/m lead
lead = 2 * 5 * 0.2
print(f"2-wire lead resistance {lead:.1f} ohm -> error {lead / (R0 * A):.2f} C")

# Type K ~41 uV/C; cold junction at 25 C
S = 41e-6
V_meas = 3.075e-3
T_hot = V_meas / S + 25
print(f"type K: {V_meas*1e3:.3f} mV with CJ at 25 C -> {T_hot:.0f} C (without CJC: {V_meas/S:.0f} C)")
# Pt100 at   0 C = 100.00 ohm
# Pt100 at 100 C = 138.51 ohm
# Pt100 at 200 C = 175.86 ohm
# 138.51 ohm -> 100.01 C
# 2-wire lead resistance 2.0 ohm -> error 5.12 C
# type K: 3.075 mV with CJ at 25 C -> 100 C (without CJC: 75 C)

Two ohms of lead resistance cause a 5 °C error on a 2-wire Pt100 — which is why industry uses 3-wire (leads cancel in a bridge) or 4-wire (Kelvin) connections. Forgetting cold-junction compensation makes a thermocouple read low by the terminal temperature. (Real type-K conversion uses the NIST ITS-90 polynomial; the linear 41 µV/°C is an approximation.)

Common mistakes

Applications

Key takeaways

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