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Electrical Temperature Instruments: Types, Formulas & Calculators

1 year ago
Last Update on April 17, 2026
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Learn thermocouples, RTDs, thermistors & digital sensors with properly rendered maths formulas, 4 interactive calculators, worked examples, and a 12-Q FAQ.

Electrical Temperature Instruments — Complete Guide with Calculators

Instrumentation Electrical Engineering Physics RTD & Thermocouple Temperature Measurement

Temperature is the single most frequently measured process variable in science, engineering, and everyday life. From smartphone chips to blast furnaces, from refrigerated vaccines to food pasteurisation, precise temperature measurement is what keeps systems safe and products up to standard. Electrical temperature instruments convert temperature into electrical signals — voltage, resistance, or digital data — making it possible to measure, monitor, and control temperature with extraordinary accuracy.

This comprehensive guide from HeLovesMath covers every major class of electrical temperature sensor: thermocouples, RTDs (Resistance Temperature Detectors), thermistors, and digital IC sensors. You will find properly rendered mathematical formulas for every operating principle, worked calculation examples, comparison tables, four interactive calculators, and a 12-question FAQ — everything you need to understand, select, and apply electrical temperature instruments.

Introduction & Temperature Measurement System Architecture

What Is Temperature?

Temperature is a scalar quantity representing the average kinetic energy of the atoms or molecules in a substance. It determines the direction of spontaneous heat flow: heat always moves from a region of higher temperature to one of lower temperature until thermal equilibrium is reached. At the microscopic level, a gas molecule at 300 K has an average translational kinetic energy given by:

✦ Kinetic Energy & Temperature
\[\overline{E_k} = \frac{3}{2}\,k_B T\]
where \(k_B = 1.380649 \times 10^{-23}\ \text{J K}^{-1}\) (Boltzmann constant) and \(T\) is absolute temperature in Kelvin.

Temperature vs. Heat vs. Thermal Energy

🌡️ Temperature

Intensity of thermal energy. Measured in °C, °F, or K. A small candle flame is hotter than a warm swimming pool, even though it has far less total heat energy.

🔥 Heat (Q)

The total thermal energy transferred between objects because of a temperature difference. Measured in Joules (J) or calories (cal). Depends on mass, specific heat capacity, and temperature change: Q = mcΔT.

⚡ Electrical Output

Electrical temperature instruments convert temperature into a measurable electrical quantity: voltage (mV for thermocouples), resistance (Ω for RTDs/thermistors), or digital bits (for digital sensors).

The Complete Temperature Measurement Chain

Every electrical temperature measurement system consists of four stages, each adding value to the raw temperature signal:

  1. Temperature Sensor: Converts the physical quantity (temperature) into a proportional electrical quantity (EMF, resistance, or current).
  2. Signal Conditioning: Amplifies the tiny sensor output, filters out electrical noise, and may linearise a non-linear response.
  3. Analogue-to-Digital Conversion (ADC): Converts the conditioned analogue voltage into a digital number for processing.
  4. Display / Control Unit: Shows the temperature value in human-readable form, logs data, or feeds a process control loop.

Key Sensor Selection Criteria

CriterionWhat It MeansTypical Specification
RangeMinimum to maximum measurable temperature−270 °C to +1820 °C (type-dependent)
AccuracyCloseness to the true temperature±0.1 °C (RTD) to ±2 °C (thermocouple)
SensitivityOutput change per °C change41 µV/°C (Type K), 0.4 Ω/°C (PT100)
Response TimeTime to reach 63.2 % of step-change valueMilliseconds to seconds
StabilityDrift over time / thermal cycles±0.01 °C/year (good RTD)
Self-HeatingTemperature rise from excitation current<0.1 °C (with proper design)

Temperature Scales & Conversion Formulas

Three temperature scales are in common use in science and engineering. Understanding their relationships is fundamental to working with any temperature sensor.

The Three Major Scales

°C — Celsius (Centigrade)

Defined so that 0 °C = melting point of water and 100 °C = boiling point of water at 1 atm. The most widely used everyday scale globally.

°F — Fahrenheit

Used primarily in the United States. 32 °F = freezing, 212 °F = boiling. One Fahrenheit degree = 5/9 of one Celsius degree.

K — Kelvin (SI Base Unit)

The thermodynamic temperature scale. 0 K = absolute zero (−273.15 °C), the lowest theoretically possible temperature. Kelvin intervals equal Celsius intervals: ΔT is the same in both scales.

Conversion Formulas

✦ Celsius ↔ Fahrenheit
\[°\text{F} = \left(°\text{C} \times \frac{9}{5}\right) + 32 \qquad \Longleftrightarrow \qquad °\text{C} = (°\text{F} - 32)\times\frac{5}{9}\]
✦ Celsius ↔ Kelvin
\[T(\text{K}) = °\text{C} + 273.15 \qquad \Longleftrightarrow \qquad °\text{C} = T(\text{K}) - 273.15\]
✦ Fahrenheit ↔ Kelvin
\[T(\text{K}) = \bigl(°\text{F} - 32\bigr)\times\frac{5}{9} + 273.15\]

Key Reference Points

Phenomenon°C°FK
Absolute Zero−273.15−459.670
Freezing Point of Water032273.15
Typical Room Temperature20–2568–77293–298
Human Normal Body Temperature3798.6310.15
Boiling Point of Water (1 atm)100212373.15
Melting Point of Iron153828001811
Surface of the Sun~5500~9932~5773
Note for Engineers: Always use Kelvin (absolute temperature) in thermodynamic equations, gas laws, and radiation calculations. Celsius or Fahrenheit can be used for differences (ΔT), but not for ratios — saying "twice as hot" requires Kelvin.

Thermocouples — The Seebeck Effect

A thermocouple is the workhorse of high-temperature industrial measurement. It consists of two wires of dissimilar metals joined at one end (the measuring junction or hot junction). When this junction is at a different temperature from the opposite end (the reference junction or cold junction), a small thermoelectric EMF (electromotive force) is produced.

The Seebeck Effect — Operating Principle

Thomas Johann Seebeck discovered in 1821 that a circuit made from two different metals — with junctions held at different temperatures — generates a continuous electric current. This is the Seebeck effect, and it is the foundation of thermocouple operation.

✦ Thermocouple Output Voltage
\[V = \alpha_{\text{AB}} \times (T_1 - T_2)\]
V = thermoelectric EMF (volts)  |  αAB = Seebeck coefficient of metal pair (V/K)  |  T₁ = measuring junction temperature (K or °C)  |  T₂ = reference junction temperature (K or °C)

In practice, thermocouple outputs are tabulated against a 0 °C reference. Real outputs are slightly non-linear; polynomial approximations are used for precision:

✦ Polynomial Approximation of Thermocouple EMF
\[E(T) = c_0 + c_1 T + c_2 T^2 + c_3 T^3 + \cdots + c_n T^n\]
where \(c_0, c_1, \ldots, c_n\) are type-specific coefficients published in IEC 60584-1, and \(T\) is temperature in °C referenced to 0 °C cold junction.

Thermocouple Types at a Glance

TypeMaterialsRange (°C)Sensitivity (µV/°C)Typical Use
KChromel / Alumel−200 to +135041General purpose — ovens, kilns, HVAC
JIron / Constantan−40 to +75055Plastics processing, reducing atmospheres
TCopper / Constantan−250 to +35043Cryogenics, food processing
EChromel / Constantan−200 to +90068Highest sensitivity — subfreezing to moderate high-T
NNicrosil / Nisil−270 to +130039High-stability alternative to Type K
SPt90Rh10 / Pt−50 to +176810Calibration standards, laboratories
RPt87Rh13 / Pt−50 to +176810Similar to Type S, higher Rh content
BPt70Rh30 / Pt94Rh60 to +182010Widest range — glass/steel furnaces

Cold Junction Compensation

A thermocouple only measures the temperature difference between its two junctions. To obtain an absolute temperature at the hot junction, the reference (cold) junction temperature must be known and compensated for. Modern transmitters measure the local ambient temperature with a separate precision sensor and add this offset electronically.

✦ Cold Junction Compensation Equation
\[T_{\text{hot}} = T_{\text{EMF measured}} + T_{\text{cold junction}}\]
Or more precisely: convert measured EMF to temperature at 0 °C reference, then add the actual cold junction temperature.
✅ Advantages
  • Widest temperature range (down to −270 °C, up to +1820 °C)
  • Self-powered — no excitation supply needed
  • Rugged, small, fast response
  • Low cost for most types
⚠️ Limitations
  • Low output voltage (µV range) — susceptible to noise
  • Non-linear response requires polynomial correction
  • Requires cold junction compensation
  • Lower accuracy than RTDs (typically ±1–2 °C)
  • Calibration drift over time (contamination of metals)
⚠️ Extension Wire Rule: Always use the correct thermocouple extension or compensating cable for your thermocouple type. Using ordinary copper wire creates parasitic junctions that introduce measurement errors equal to the temperature difference at those junctions.

RTDs — Resistance Temperature Detectors

RTDs exploit the well-known relationship between temperature and the electrical resistivity of pure metals. As temperature rises, increased atomic vibration scatters conduction electrons more frequently, raising resistance. Platinum is the preferred material because of its exceptional chemical stability, repeatability, and near-linear response across a wide range.

Basic RTD Equation — Linear Approximation

✦ RTD Resistance (Linear Approximation)
\[R(t) = R_0\,\left(1 + \alpha\, t\right)\]
R(t) = resistance at temperature \(t\) (Ω)  |  R₀ = resistance at 0 °C (100 Ω for PT100, 1000 Ω for PT1000)  |  α = temperature coefficient of resistance for platinum ≈ 0.003850 Ω/(Ω·°C) (IEC 60751)  |  t = temperature (°C)

Callendar–Van Dusen Equation (High Accuracy)

For precision applications, the linearised formula is insufficient. The full Callendar–Van Dusen equation is used:

✦ Callendar–Van Dusen (IEC 60751)
\[\text{For } t \geq 0\,°\text{C}: \quad R(t) = R_0\!\left(1 + A\,t + B\,t^2\right)\] \[\text{For } t < 0\,°\text{C}: \quad R(t) = R_0\!\left[1 + A\,t + B\,t^2 + C\,(t-100)\,t^3\right]\]
IEC 60751 platinum constants: \(A = 3.9083 \times 10^{-3}\ °\text{C}^{-1}\), \(B = -5.775 \times 10^{-7}\ °\text{C}^{-2}\), \(C = -4.183 \times 10^{-12}\ °\text{C}^{-4}\)

PT100 vs PT1000

PT100

100 Ω at 0 °C — Sensitivity ≈ 0.385 Ω/°C. Most common industrial standard. Higher excitation current (1–5 mA) makes it susceptible to self-heating errors over long cable runs.

PT1000

1000 Ω at 0 °C — Sensitivity ≈ 3.85 Ω/°C. Smaller excitation current needed (100 µA), reducing self-heating. Better for long cable runs or battery-powered applications.

RTD Wiring Configurations

ConfigurationWiresLead CompensationAccuracyUse Case
2-Wire2None — lead resistance adds errorLowestShort cables, non-critical
3-Wire3Partial — assumes equal lead resistanceGoodMost industrial applications
4-Wire (Kelvin)4Complete — separate I and V pathsHighestPrecision / calibration labs
✦ 4-Wire Kelvin Measurement Principle
\[R_{\text{RTD}} = \frac{V_{\text{measured}}}{I_{\text{source}}}\]
A precision constant current source forces current through two outer leads, while the voltage is measured across the RTD using two inner leads that carry negligible current — completely eliminating lead resistance errors.

Thermistors — NTC & PTC Types

Thermistors are semiconductor resistors whose resistance changes dramatically with temperature. Unlike the relatively small, predictable changes in metals (used for RTDs), thermistors exhibit large, non-linear resistance changes — which can be either useful (NTC types for high-sensitivity sensing) or protective (PTC types for circuit protection).

NTC Thermistor — Beta Equation

✦ NTC Thermistor — Beta (β) Model
\[R(T) = R_0 \cdot \exp\!\left[\beta\!\left(\frac{1}{T} - \frac{1}{T_0}\right)\right]\]
R(T) = resistance at absolute temperature T (Ω)  |  R₀ = resistance at reference temperature T₀ (usually 25 °C = 298.15 K)  |  β = Beta constant of the thermistor material (K), typically 2000–5000 K  |  T, T₀ = temperatures in Kelvin

Steinhart–Hart Equation (Higher Accuracy)

For precision work over a wide range, the three-parameter Steinhart–Hart equation is superior:

✦ Steinhart–Hart Equation
\[\frac{1}{T} = A + B\ln(R) + C\bigl(\ln(R)\bigr)^3\]
T = temperature in Kelvin  |  R = thermistor resistance (Ω)  |  A, B, C = Steinhart–Hart coefficients, determined by measuring R at three calibration temperatures.

NTC Thermistor Sensitivity

An important derived quantity is the temperature coefficient of resistance (α) for an NTC thermistor at a given temperature:

✦ NTC Temperature Coefficient α (at temperature T)
\[\alpha(T) = -\frac{\beta}{T^2} \quad (\text{units: }°\text{C}^{-1}\text{ or K}^{-1})\]
Example: for β = 3950 K at T = 298.15 K (25 °C): α = −3950/298.15² ≈ −0.0444 per °C (4.44 % per °C). This is roughly 11× more sensitive than a platinum RTD.

PTC Thermistors

PTC (Positive Temperature Coefficient) thermistors exhibit a dramatic, non-linear increase in resistance above a threshold (Curie) temperature. They are primarily used as self-resetting fuses, motor overheating protectors, and self-regulating heaters — not for precision temperature measurement.

NTC — Sensing Applications
  • Medical thermometers
  • Automotive engine temperature
  • Battery packs & thermal management
  • HVAC room sensors
PTC — Protection Applications
  • Overcurrent protection (polyfuses)
  • Motor winding protection
  • Self-regulating heating elements
  • Telecom line protection

Digital Temperature Sensors

Digital temperature sensors integrate the sensing element, signal conditioning, ADC, and digital interface into a single IC (integrated circuit). They output temperature directly as a digital number, eliminating the need for external signal processing.

I²C Interface

2-wire serial bus (SDA + SCL). Multiple sensors share one bus using unique addresses. Examples: TMP102, LM75, MCP9808. Resolution: 0.0625 °C to 0.25 °C. Range: −55 °C to +125 °C typical.

1-Wire Interface

Single data wire (+ optional parasitic power). Unique 64-bit serial number on each sensor. Example: DS18B20 — the most cloned temperature sensor ever. Range: −55 °C to +125 °C, accuracy ±0.5 °C, programmable 9–12 bit resolution.

SPI Interface

4-wire fast synchronous bus (MOSI, MISO, SCK, CS). Used for thermocouple digitisers (MAX31855 for Type K; MAX31865 for RTDs), providing cold junction compensation on-chip.

Why Use Digital Sensors? For microcontroller-based systems (Arduino, Raspberry Pi, STM32), digital sensors eliminate ADC circuitry entirely. A DS18B20 on a single GPIO pin can report temperature to 0.0625 °C without any analogue components. Multiple sensors can even share the same wire using 1-Wire's ROM addressing.

Infrared & Non-Contact Temperature Sensors

All objects above absolute zero emit thermal radiation (electromagnetic radiation with wavelengths from ≈ 700 nm into the far infrared). The amount and spectral distribution of this radiation depends on the object's temperature — a relationship described by the Stefan‑Boltzmann Law and Planck's radiation formula.

✦ Stefan–Boltzmann Law (Total Radiated Power)
\[P = \varepsilon \,\sigma\, T^4\]
P = radiated power per unit area (W/m²)  |  ε = emissivity of the surface (0 = perfect mirror; 1 = perfect blackbody)  |  σ = Stefan–Boltzmann constant = \(5.6704 \times 10^{-8}\ \text{W m}^{-2}\text{K}^{-4}\)  |  T = absolute temperature in Kelvin
✦ Wien's Displacement Law (Peak Emission Wavelength)
\[\lambda_{\max} = \frac{b}{T} \qquad b = 2.898 \times 10^{-3}\ \text{m·K}\]
At 37 °C (310 K): \(\lambda_{\max} = 2.898\times10^{-3}/310 \approx 9.35\ \mu\text{m}\) — deep infrared, the basis of medical IR ear/forehead thermometers.
💡 Emissivity Matters: IR thermometers must be set to the correct emissivity of the target material. Human skin: ε ≈ 0.98. Polished aluminium: ε ≈ 0.05. Failing to account for emissivity causes large measurement errors on reflective surfaces.

Comprehensive Sensor Comparison Table

PropertyThermocoupleRTD (PT100)NTC ThermistorDigital ICIR Sensor
Temperature Range−270 to +1820 °C−200 to +850 °C−100 to +300 °C−55 to +150 °C−70 to +1000+ °C
Accuracy (typical)±1–2 °C±0.1–0.5 °C±0.2–0.5 °C±0.5–2 °C±0.5–2 °C
Output TypeµV voltageResistance (Ω)Resistance (Ω)Digital (bits)Digital / analogue
Sensitivity41–68 µV/°C0.385 Ω/°CVery high (non-linear)CalibratedBased on IR power
Self-powered?YesNo (needs excitation)No (needs excitation)No (needs VCC)No (needs VCC)
Long-term StabilityFairExcellentGoodGoodGood
Contact Required?YesYesYesYesNo
Relative CostLow–MediumMediumLowLow–MediumMedium–High
ComplexityMedium (CJC needed)Low–MediumLowVery LowLow (IR corrections)

Temperature Range Visualisation

Thermocouple −270 °C to +1820 °C
RTD (PT100) −200 °C to +850 °C
NTC Thermistor −100 °C to +300 °C
Digital IC Sensor −55 °C to +150 °C

Interactive Electrical Temperature Calculators

Use the tabs below to access all four calculators. Each one applies the exact mathematical formula from the sections above.

🌡️ Temperature Unit Converter (°C / °F / K)

Formula used
\[°\text{F} = \left(°\text{C} \times \tfrac{9}{5}\right)+32 \quad;\quad T_K = °\text{C}+273.15\]

📊 RTD Resistance Calculator (PT100 / PT1000)

Formula used
\[R(t) = R_0\bigl(1 + At + Bt^2\bigr) \quad (t \geq 0\,°\text{C})\]
A = 3.9083 × 10⁻³, B = −5.775 × 10⁻⁷, α ≈ 0.003850 Ω/(Ω·°C)

⚡ Thermocouple Output Voltage Calculator

Formula used (linear approximation)
\[V = \alpha_{\text{TC}}\times(T_1 - T_2)\]
αTC = Seebeck coefficient in µV/°C (sensor-type dependent). Result converted to millivolts.

🔩 NTC Thermistor Resistance Calculator (Beta Equation)

Formula used
\[R(T) = R_{25} \cdot \exp\!\left[\beta\!\left(\frac{1}{T}-\frac{1}{298.15}\right)\right]\]
T is temperature in Kelvin (T = °C + 273.15). R₂₅ and β are from the sensor datasheet.

Worked Examples

Example 1 — Temperature Conversion: 450 °F to Kelvin

1
Write down the conversion formula: \(T(\text{K}) = (°F - 32)\times\tfrac{5}{9} + 273.15\)
2
Subtract 32 from 450: \(450 - 32 = 418\)
3
Multiply by 5/9: \(418 \times \tfrac{5}{9} = 232.22\ °C\)
4
Add 273.15: \(232.22 + 273.15 = 505.37\ \text{K}\)

✅ Answer: 450 °F = 232.22 °C = 505.37 K

Example 2 — PT100 RTD Resistance at 220 °C (Callendar–Van Dusen)

1
Since t = 220 °C ≥ 0, use: \(R(t) = R_0(1 + At + Bt^2)\)
2
Substitute A = 3.9083×10⁻³, B = −5.775×10⁻⁷, R₀ = 100 Ω, t = 220:
\(At = 3.9083\times10^{-3}\times220 = 0.85983\)
3
\(Bt^2 = -5.775\times10^{-7}\times(220)^2 = -5.775\times10^{-7}\times 48400 = -0.027951\)
4
\(R(220) = 100 \times (1 + 0.85983 - 0.027951) = 100 \times 1.83188 = 183.19\ \Omega\)

✅ Answer: PT100 resistance at 220 °C ≈ 183.19 Ω

Example 3 — Type K Thermocouple Output at 800 °C (25 °C reference)

1
Type K Seebeck coefficient α = 41 µV/°C
2
Temperature difference: \(T_1 - T_2 = 800 - 25 = 775\ °C\)
3
Output: \(V = 41\ \mu\text{V/°C} \times 775\ °C = 31{,}775\ \mu\text{V} = 31.775\ \text{mV}\)
4
Note: The NIST polynomial for Type K gives 32.868 mV at 800 °C (0 °C reference). The linear approximation is close but slightly off for large ranges.

✅ Answer: ≈ 31.8 mV (linear) / 32.87 mV (NIST polynomial)

Example 4 — NTC Thermistor Resistance at 75 °C (R₂₅ = 10 kΩ, β = 3950 K)

1
Convert temperatures: T = 75 + 273.15 = 348.15 K; T₀ = 25 + 273.15 = 298.15 K
2
Calculate the exponent: \(\!\beta\!\left(\tfrac{1}{T}-\tfrac{1}{T_0}\right) = 3950\!\left(\tfrac{1}{348.15}-\tfrac{1}{298.15}\right)\)
3
\(= 3950 \times (0.002872 - 0.003354) = 3950 \times (-0.000482) = -1.9039\)
4
\(R(75) = 10{,}000 \times e^{-1.9039} = 10{,}000 \times 0.1490 = 1{,}490\ \Omega\)

✅ Answer: NTC thermistor resistance at 75 °C ≈ 1,490 Ω (compared to 10,000 Ω at 25 °C — a 6.7× reduction)

Frequently Asked Questions

An electrical temperature instrument converts temperature into a proportional electrical quantity — voltage (thermocouple), resistance (RTD, thermistor), or a digital output (IC sensor) — so the reading can be measured, recorded, and used to control processes automatically.
The Seebeck effect is the generation of an EMF in a circuit of two dissimilar conductors when their junctions are at different temperatures. The output voltage follows \(V = \alpha(T_1 - T_2)\), where α is the Seebeck coefficient. It allows thermocouples to be self-powered — no battery or excitation source is required.
Both are platinum RTDs with the same fundamental behaviour. PT100 has a base resistance of 100 Ω at 0 °C; PT1000 has 1000 Ω at 0 °C. PT1000 offers 10× higher resistance, so lead wire resistance matters far less, making it better for long cable runs and low-power applications. PT100 is the dominant industrial standard.
RTDs use pure metals — electrons scatter off atomic vibrations, giving a modest, nearly linear resistance increase (α ≈ +0.39 % per °C for platinum). NTC thermistors use semiconductor materials where charge carrier concentration changes exponentially with temperature, giving sensitivity of 4–6 % per °C — over 10 times greater. This comes at the cost of highly non-linear response.
Simply add 273.15: \(K = °C + 273.15\). For quick mental maths, add 273. For example, 100 °C = 373.15 K (exact). Zero Kelvin (absolute zero) corresponds to −273.15 °C — the lowest temperature physically achievable.
Type K (Chromel-Alumel) is by far the most common, covering −200 °C to +1350 °C with a sensitivity of 41 µV/°C. It is inexpensive, widely available, and suitable for most general industrial applications including ovens, kilns, HVAC, and process heating. Type J is common in older plastics-processing equipment. Type T is preferred for cryogenic applications.
A thermocouple only measures the temperature difference between its hot and cold junctions. Cold junction compensation (CJC) adds the ambient temperature of the cold junction (measured by a separate precision sensor) to the indicated temperature, converting a differential reading into an absolute temperature. Without CJC, a Type K thermocouple would read 0 mV at 25 °C if its reference is also at 25 °C — giving the wrong impression that the measurement point is at 0 °C.
Emissivity (ε, 0–1) describes how efficiently a surface emits thermal radiation compared to a perfect blackbody. IR thermometers must be configured with the correct emissivity for each surface. Human skin ≈ 0.98; polished stainless steel ≈ 0.12. Using the wrong emissivity causes large errors: if a polished metal surface is treated as a blackbody, the indicated temperature will be far too low because most of the "radiation" being detected is reflected energy from the environment, not emission from the surface itself.
When an excitation current flows through an RTD, it dissipates power \(P = I^2 R\), raising the element's own temperature above its surroundings. This causes a positive measurement error. For a typical PT100 with 1 mA excitation: P = (0.001)² × 100 = 0.1 mW — negligible in well-ventilated air but significant in still oil or in a vacuum. Minimise it by: (1) using the smallest practical excitation current (100 µA for PT1000), (2) pulsed measurement techniques, (3) choosing larger-mass RTD housings, and (4) ensuring good thermal contact between sensor and medium.
The time constant τ (tau) is the time required for a sensor's reading to reach 63.2 % of the final value following a step change in temperature. After 5τ, the sensor has settled to within 0.7 % of the final value. Bare‑wire thermocouples can have τ as short as a few milliseconds in a flowing liquid, while a heavy thermowell assembly might have τ of several minutes. Thermistors with small beads also offer very fast response (seconds in air).
The Callendar–Van Dusen equation accurately describes platinum RTD resistance across their full operating range. For t ≥ 0 °C: \(R(t) = R_0(1+At+Bt^2)\). For t < 0 °C: \(R(t) = R_0[1+At+Bt^2+C(t-100)t^3]\). Using the IEC 60751 constants (A = 3.9083×10⁻³, B = −5.775×10⁻⁷, C = −4.183×10⁻¹²), error versus the simple linear formula is less than 0.05 Ω across the full −200 °C to +850 °C range.
Choose digital sensors (like DS18B20 or TMP102) when: (1) you are connecting directly to a microcontroller and want to avoid signal conditioning; (2) temperature range is moderate (−55 °C to +125 °C); (3) multiple sensors share one wire; (4) system needs internal alarms or registers. Choose thermocouples for extreme temperatures (>200 °C or <−200 °C) or harsh environments. Choose RTDs when long-term stability and high accuracy (±0.1 °C) are critical, such as in calibration labs, pharmaceutical storage, or precision HVAC.
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