Temperature measurement

In short

Temperature measurement is the inference of a body's thermal state from a measurable physical change — expansion, electrical resistance, thermo-emf, or emitted radiation — since temperature itself cannot be measured by comparison with a standard mass or length. It is the most widely measured process variable in industry: roughly half of all field instruments in a refinery, power station or pharmaceutical plant are temperature sensors. Indian employers such as NTPC, BHEL, IOCL, ONGC, Tata Steel, L&T, Honeywell, Emerson, Yokogawa, ABB and Siemens test it in campus interviews through thermocouple and RTD selection, cold-junction compensation, lead-wire errors and loop calibration. In exams it carries steady marks in GATE (IN and EE), ESE and university Sensors/Instrumentation papers, usually as numerical problems on RTD resistance, thermo-emf and radiation laws.

Explained

Scales, standards and classification

• Temperature is the intensive property that decides the direction of heat flow; the Zeroth Law makes thermometry possible — two bodies in equilibrium with a third are in equilibrium with each other.
• Scales: Celsius (°C), Kelvin (K, SI base unit), Fahrenheit (°F), Rankine (°R). T(K) = t(°C) + 273.15; t(°F) = 1.8 t(°C) + 32.
• Since 20 May 2019 the kelvin is defined by fixing the Boltzmann constant k = 1.380649 × 10⁻²³ J/K, not by the triple point of water (which is now a measured value, 273.16 K with uncertainty).
• ITS-90 (International Temperature Scale of 1990) is the practical realisation: defined fixed points (triple point of water 0.01 °C, freezing points of tin 231.928 °C, zinc 419.527 °C, aluminium 660.323 °C, silver 961.78 °C) with specified interpolating instruments — standard platinum resistance thermometer up to 961.78 °C, radiation thermometry above it. CSIR–NPL, New Delhi maintains the national temperature standard in India; NABL-accredited labs provide traceable calibration.
• Contact versus non-contact: contact sensors must reach thermal equilibrium with the medium; non-contact (radiation) sensors read emitted infrared and need no equilibrium.
• Primary versus secondary: a gas thermometer is primary (reading derived from first principles); thermocouples, RTDs and thermistors are secondary (need calibration).

Expansion thermometers

• Liquid-in-glass: mercury (−38 to +356 °C, extendable to ~550 °C with nitrogen fill) or alcohol/kerosene with dye (−80 to +70 °C). Simple, no power, but fragile, local reading only, and mercury is restricted — India ratified the Minamata Convention in 2018, and mercury thermometers are being phased out of healthcare and industry.
• Errors: emergent-stem error (the stem is cooler than the bulb), parallax, time lag, and non-uniform bore.
• Bimetallic strip: two metals of different expansion coefficients (invar and brass/steel) bonded together; heating bends the strip. Wound as a helix or spiral to drive a pointer. Range about −40 to 550 °C, accuracy ±1–2% of span. Used in dial thermometers, oven and geyser thermostats, and overload relays.
• Filled-system (capillary) thermometers — Class I liquid-filled, Class II vapour-pressure, Class III gas-filled (nitrogen), Class V mercury-filled. A bulb, capillary and Bourdon element give remote indication up to ~60 m without electricity — still used on transformers (oil and winding temperature indicators, WTI/OTI) and boiler drums.
• Vapour-pressure type follows the Clausius–Clapeyron relation, so its scale is non-linear (crowded at the low end) but it needs no ambient compensation because only the bulb liquid–vapour interface matters.

Thermocouples

• Seebeck effect: a closed circuit of two dissimilar metals with junctions at different temperatures generates an emf. The emf arises along the wires wherever a temperature gradient exists, not "at the junction" — the junction merely closes the loop.
• Supporting effects: Peltier (heat absorbed/released at a junction carrying current — reversible) and Thomson (heat exchange along a single conductor with a gradient).
• Laws of thermoelectricity:
  1. Law of homogeneous circuit — no emf in a circuit of a single homogeneous metal, however heated; so emf depends on the pair, not on wire length or diameter.
  2. Law of intermediate metals — inserting a third metal does not change the emf provided its two ends are at the same temperature; this is why copper lead wires, terminal blocks and solder joints are allowed.
  3. Law of intermediate temperatures — E(T₁,T₃) = E(T₁,T₂) + E(T₂,T₃); this is the basis of cold-junction compensation and of using tables referenced to 0 °C.
• Common types (IEC 60584-1 characteristics; colour codes differ between IEC and ANSI — in India IEC/IS colour coding is normally specified):
  • K (Chromel–Alumel): −200 to 1,260 °C, ~41 µV/°C, the industrial workhorse; avoid 800–1,050 °C in reducing/sulphurous atmospheres (green rot).
  • J (Iron–Constantan): 0 to 760 °C, ~55 µV/°C; iron leg rusts.
  • T (Copper–Constantan): −200 to 350 °C, ~43 µV/°C; best for cryogenic and low-range work.
  • E (Chromel–Constantan): highest output of standard types, ~68 µV/°C.
  • N (Nicrosil–Nisil): better high-temperature stability than K.
  • R, S (Pt-13%Rh/Pt, Pt-10%Rh/Pt): up to ~1,600 °C, low output ~10 µV/°C; B (Pt-30%Rh/Pt-6%Rh) up to ~1,700 °C, unusable below ~250 °C.
• Cold-junction compensation (CJC): tables assume the reference junction at 0 °C. Methods — ice bath (laboratory standard), a measured reference block with a thermistor/RTD and software correction (modern transmitters, DAQ cards), or a bridge-based compensating-lead network.
• Extension versus compensating cable: extension cable is of the same alloys as the thermocouple (for K, J, T, E); compensating cable of cheaper alloys with a matching emf curve over a limited range is used for R, S, B. Never use copper to extend a thermocouple — the effective measuring junction moves to the terminal block.
• Construction: grounded junction (fast, but no electrical isolation), ungrounded/insulated (isolated, slightly slower), exposed (fastest, for gases only). Mineral-insulated metal-sheathed (MIMS) probes are standard; sheath materials Inconel 600, SS 316, SS 310.
• Advantages: wide range, rugged, small and fast, self-generating (no excitation), cheap. Limitations: low output (mV), non-linear, needs CJC and special cable, poor for small differences, and drifts with contamination and cold-work.

Resistance thermometers (RTDs) and thermistors

• RTD principle: metallic resistance rises nearly linearly with temperature. Platinum is standard — chemically inert, wide range, repeatable.
• Pt100 = 100.00 Ω at 0 °C; Pt1000 gives ten times the sensitivity and makes lead resistance relatively less important. IEC 60751 / IS 2806 fix the characteristic with α = 0.00385 Ω/Ω/°C (industrial grade) and tolerance classes AA (±0.1 + 0.0017|t| °C), A, B (±0.3 + 0.005|t| °C), C.
• Callendar–Van Dusen equation describes the curve: for t ≥ 0 °C, R(t) = R₀[1 + At + Bt²]; below 0 °C a (t−100)t³ term is added. For α = 0.00385: A = 3.9083 × 10⁻³, B = −5.775 × 10⁻⁷, C = −4.183 × 10⁻¹².
• Range: −200 to 650 °C industrially (850 °C for some sheathed types). Other metals: nickel (cheap, non-linear, to 300 °C), copper (very linear, to 150 °C), tungsten (very high temperature).
• Lead-wire compensation:
  • 2-wire — lead resistance adds directly to the measurement; a 1 Ω total lead adds about 2.6 °C error on a Pt100.
  • 3-wire — the bridge cancels lead resistance provided the two legs are equal; the industry default.
  • 4-wire (Kelvin) — constant current through two leads, voltage sensed through the other two; lead resistance cancels completely. Used for standards and critical duty.
• Self-heating: I²R in the element raises its own temperature; excitation is kept to 1 mA or less. Self-heating error = I²R × S, where S is the dissipation constant (°C/mW) and depends on the medium — worst in still air.
• Thermistor: sintered metal-oxide semiconductor. NTC types dominate measurement; resistance falls steeply and exponentially with temperature, giving very high sensitivity (−3 to −6 %/°C) but a narrow, strongly non-linear range (−80 to about 300 °C). PTC types are used as switches, self-regulating heaters and inrush limiters.
• Steinhart–Hart / beta model linearises a thermistor over a limited span. Thermistors are used in motor-winding protection (PTC in three-phase motors, per IEC/IS standards), transformer-oil probes, battery management systems and medical thermometers.
• Semiconductor IC sensors: the base-emitter voltage of a diode/transistor falls about 2 mV/°C. LM35 (10 mV/°C, direct in °C), AD590 (1 µA/K), DS18B20 (digital, 1-Wire). Range −55 to 150 °C, cheap and linear, used on PCBs and in embedded projects.

Non-contact (radiation) thermometry

• Every body above absolute zero radiates; the sensor infers temperature from the radiant flux.
• Stefan–Boltzmann law: E = εσT⁴ — total emissive power. Wien's displacement law: λ_max T = 2898 µm·K — the peak wavelength shifts shorter as temperature rises, which is why a hot body glows red then white.
• Total radiation pyrometer: a lens/mirror focuses all wavelengths on a blackened thermopile; output ∝ T⁴. Range about 0–2,000 °C, needs emissivity correction and a clean sight path.
• Optical (disappearing-filament) pyrometer: the operator varies the current in a tungsten filament until it vanishes against the hot background at 0.65 µm; brightness temperature read from the lamp current. Range ~700–3,000 °C; manual, used in foundries and for calibration.
• Infrared thermometer / thermal imager: photon or thermopile detector with emissivity setting, measures at a fixed IR band; distance-to-spot ratio (D:S) fixes the smallest target measurable at a given distance.
• Two-colour (ratio) pyrometer: takes the ratio of radiance at two wavelengths, so emissivity, dust, smoke and a partly obscured view largely cancel — used on steel furnaces and cement kilns.
• Emissivity is the key error source: ε ≈ 0.95 for oxidised steel, brick and paint; 0.05–0.1 for polished aluminium or steel, which read far too low. Reflected background radiation and intervening CO₂/water vapour absorption also bias the reading.
• Advantages: no contact, no upper range limit in practice, very fast (ms), suitable for moving or live targets. Limitations: measures surface only, emissivity and sight-path dependent, costly, no use inside opaque vessels.

Installation, signal conditioning and dynamics

• Thermowell: a closed-end tube letting the sensor be replaced without breaking process containment; adds thermal lag. Material SS 316, Monel, Inconel; types threaded, flanged, socket-weld; drilled bar stock for high pressure. Insertion depth should be about 10× the well diameter (and at least past the boundary layer) to limit stem conduction error.
• Wake-frequency (vortex-shedding) calculation per ASME PTC 19.3 TW checks the well will not resonate in flowing fluid — an exam-favourite failure mode in steam lines.
• Signal conditioning: thermocouple mV or RTD bridge → instrumentation amplifier → linearisation → 4–20 mA two-wire transmitter, or digital HART / Foundation Fieldbus / Modbus. Field-mounted smart transmitters do CJC, linearisation, sensor-break detection and dual-sensor backup.
• Noise: use shielded twisted pair, single-point earth, separate routing from power cables; RTD and thermocouple circuits are high-impedance, low-level and pick up 50 Hz hum — hence mains-frequency-rejecting integrating ADCs.
• Dynamic response: a sensor in a well behaves as a first-order system, τ = mc/hA. Response to a step: T(t) = T_f + (T_i − T_f)e^−t/τ; the sensor reaches 63.2% in one τ and about 99% in 5τ. Reduce τ with a thin sheath, good contact (heat-conducting paste or oil in a dry well), and higher fluid velocity.
• Safety and statutory practice (India): boilers and pressure parts come under the Indian Boiler Regulations, 2026 (in force from October 2026, superseding the 1950 Regulations), framed under the Boilers Act, 2025 (in force from 1 May 2025, replacing the Boilers Act, 1923), with temperature/pressure instruments and their calibration inspected by the state Boiler Inspectorate. Hazardous areas need Ex d/Ex ia certified transmitters (IS/IEC 60079 series) with PESO/CCOE approval. Workplace thermal and instrument-safety duties now sit under the Occupational Safety, Health and Working Conditions Code, 2020, in force from 21 November 2025, which replaced the Factories Act, 1948. Legal metrology verification of measuring instruments used in trade falls under the Legal Metrology Act, 2009.

Key points

• Zeroth Law - the basis of all thermometry; equality of temperature means thermal equilibrium.
• Kelvin (since 2019) - defined by fixing the Boltzmann constant at 1.380649 × 10⁻²³ J/K; ITS-90 is the practical scale realised in India by CSIR–NPL.
• Seebeck effect - emf generated by a temperature gradient in a circuit of two dissimilar metals; the thermocouple's working principle.
• Law of intermediate metals - a third metal with both ends at the same temperature adds no emf; allows copper leads and terminal blocks.
• Law of intermediate temperatures - E(T₁,T₃) = E(T₁,T₂) + E(T₂,T₃); the basis of cold-junction compensation.
• Cold-junction compensation - thermocouple tables assume 0 °C reference; without CJC the reading is offset by the ambient temperature's equivalent emf.
• Type K - Chromel–Alumel, ~41 µV/°C, −200 to 1,260 °C, the general industrial choice; R/S/B for above 1,200 °C.
• Pt100 / IEC 60751, IS 2806 - 100 Ω at 0 °C, α = 0.00385, classes AA/A/B/C; the standard industrial RTD.
• Callendar–Van Dusen - R(t) = R₀(1 + At + Bt²) above 0 °C; defines RTD non-linearity.
• 3-wire RTD - cancels lead resistance in the bridge; 2-wire adds about 2.6 °C per ohm of lead on a Pt100; 4-wire is best.
• Self-heating - I²R in the RTD element; keep excitation ≤1 mA and allow for the dissipation constant.
• Thermistor - NTC metal oxide, very high sensitivity but exponential and narrow-range; PTC used for motor-winding protection.
• Stefan–Boltzmann - E = εσT⁴, σ = 5.67 × 10⁻⁸ W/m²K⁴; the total-radiation pyrometer law.
• Wien's law - λ_max T = 2898 µm·K; fixes the band an IR thermometer must use.
• Emissivity - the dominant error in non-contact measurement; a ratio (two-colour) pyrometer largely cancels it.
• Thermowell - allows sensor replacement without opening the process, at the cost of thermal lag; insertion ≈10× well diameter.
• Time constant τ = mc/hA - 63.2% of a step in one τ, ~99% in 5τ; mass and poor contact slow the sensor.
• 4–20 mA / HART - the standard transmission for field temperature signals; live zero lets a broken loop be detected.

Formulas and examples

1. Pt100 resistance and the error of ignoring non-linearity. Find R at 200 °C by the linear and the CVD forms.

• Linear: R = 100(1 + 0.00385 × 200) = 100 × 1.77 = 177.00 Ω.
• CVD: A·t = 3.9083×10⁻³ × 200 = 0.781660; B·t² = −5.775×10⁻⁷ × 40,000 = −0.023100. Sum = 0.758560 → R = 175.856 Ω.
• Difference 1.144 Ω. Local sensitivity near 200 °C = R₀(A + 2Bt) ≈ 0.368 Ω/°C, so the linear formula would over-read by about 3.1 °C — why instruments use CVD or a lookup table.

2. Two-wire lead error on a Pt100. 100 m run of 0.5 mm² copper, resistivity 1.72 × 10⁻⁸ Ω·m, loop length 200 m.

• R_lead = 1.72×10⁻⁸ × 200 / (0.5×10⁻⁶) = 6.88 Ω.
• Near 0 °C the Pt100 slope is 0.3851 Ω/°C → error = 6.88/0.3851 ≈ +17.9 °C. With Pt1000 the slope is 3.851 Ω/°C, so the same lead gives only +1.8 °C — and a 3-wire connection removes it almost entirely.

3. Thermocouple with cold junction not at 0 °C. A Type K couple in a furnace; the instrument (no CJC) reads 20.64 mV; the terminal block is at 35 °C. From Type K tables, E(35 °C, 0 °C) ≈ 1.40 mV.

• By the law of intermediate temperatures, E(T_hot, 0 °C) = 20.64 + 1.40 = 22.04 mV.
• Type K table: 22.04 mV ≈ 532 °C. Ignoring compensation would have given about 500 °C — an error of roughly 33 °C, i.e. essentially the ambient temperature, because K's sensitivity near ambient and near 500 °C are both about 41 µV/°C.

4. Emissivity error in a total-radiation pyrometer. A pyrometer calibrated for a blackbody sights a surface at a true 1,000 °C (1,273.15 K) with ε = 0.85.

• Apparent temperature T_a = T_true × ε^0.25 = 1,273.15 × 0.85^0.25. ln0.85 = −0.16252; /4 = −0.04063; e^−0.04063 = 0.96019.
• T_a = 1,273.15 × 0.96019 ≈ 1,222.5 K = 949.4 °C — an under-read of about 50 °C. Setting ε = 0.85 on the instrument recovers the true value.

5. Sensor dynamics and 4–20 mA scaling. A thermowell-mounted RTD has τ = 12 s. The process steps from 30 °C to 150 °C. Transmitter range 0–200 °C.

• At t = 12 s: T = 150 + (30 − 150)e⁻¹ = 150 − 120 × 0.36788 = 105.9 °C (63.2% of the step).
• At t = 30 s: e^−2.5 = 0.08208 → T = 150 − 120 × 0.08208 = 140.2 °C.
• Time to within 1 °C of final: 120·e^−t/τ = 1 → t = 12·ln120 = 12 × 4.787 ≈ 57.4 s.
• Output at 140.2 °C: I = 4 + 16 × 140.2/200 = 4 + 11.22 = 15.22 mA.

Where it is used

• Thermal power and process plants: NTPC and refinery units use Type K/N couples on furnace and flue-gas duties, Pt100 for feedwater, bearing and winding temperatures, feeding DCS loops (Yokogawa Centum, Honeywell Experion, ABB 800xA) — a core job for instrumentation engineers and C&I technicians.
• Steel, cement and glass: two-colour and optical pyrometers on blast furnaces, ladles, kilns and float lines at Tata Steel, JSW, SAIL and UltraTech, where contact sensors would not survive.
• Pharmaceutical and food cold chain: validated Pt100 mapping of autoclaves, lyophilisers, stability chambers and vaccine cold rooms under GMP/Schedule M and WHO PQS requirements; data loggers on reefer trucks.
• Automotive and appliances: NTC thermistors for coolant, intake-air, battery-pack and HVAC sensing; bimetallic thermostats in geysers and irons; Type K probes on exhaust and brake testing at Maruti, Tata Motors and Bosch.
• Transformers and switchgear: oil and winding temperature indicators (capillary filled systems), PTC/RTD winding sensors with alarm and trip contacts, and IR thermography surveys of substations and panels — a standard preventive-maintenance service in India.
• Calibration and metrology roles: dry-block and oil-bath calibration, ice-point reference, NABL-accredited laboratories, instrument-engineer and QA posts handling traceability to CSIR–NPL.

Interview questions

• Q: Why is cold-junction compensation necessary for a thermocouple? A: The thermocouple produces an emf proportional to the difference between hot and cold junctions, and standard tables are referenced to 0 °C; unless the reference junction temperature is known and added back, the reading is offset by roughly the ambient temperature.
• Q: Where exactly is the emf generated in a thermocouple? A: Along the wires, wherever a temperature gradient exists — the junction only completes the circuit, which is why wire length and gauge do not affect the output but an in-line temperature gradient in inhomogeneous wire does.
• Q: Why is a 3-wire RTD connection preferred over 2-wire? A: The third wire lets the bridge subtract an equal lead resistance from the opposite arm, cancelling lead-wire error, which otherwise adds about 2.6 °C per ohm on a Pt100.
• Q: Why does a Pt1000 suffer less from lead resistance than a Pt100? A: Its sensitivity is ten times larger (3.851 Ω/°C against 0.3851 Ω/°C near 0 °C), so the same lead resistance corresponds to one-tenth the temperature error.
• Q: What is self-heating in an RTD and how do you limit it? A: The excitation current dissipates I²R in the element and raises its own temperature; it is limited by keeping the current at or below about 1 mA, using pulsed excitation, and ensuring good heat transfer to the medium.
• Q: When would you pick a thermocouple over an RTD? A: Above about 650 °C, where fast response or a very small or rugged probe is needed, or where no excitation supply is available; an RTD wins below that for accuracy, stability and linearity.
• Q: Why must a thermocouple never be extended with ordinary copper wire? A: The copper-to-alloy joints at the terminal block become new junctions, so the instrument measures the terminal block temperature instead of the process; extension or compensating cable of matching emf characteristic must be used.
• Q: An IR thermometer reads much lower than a contact probe on a polished steel pipe. Why? A: Polished metal has very low emissivity (0.05–0.1) and reflects background radiation, so the radiant flux reaching the detector is far less than that of a blackbody at the same temperature; painting or taping the spot, or using a ratio pyrometer, fixes it.
• Q: What does a thermowell cost you? A: Process-safe sensor replacement is gained at the cost of extra thermal mass and an air gap, which increase the time constant and can introduce stem-conduction error if insertion depth is inadequate.
• Q: A temperature loop reads 3.6 mA. What does that tell you? A: It is below the 4 mA live zero, so it is a diagnostic state — typically sensor burnout or open circuit driving the transmitter downscale — not a valid temperature.
• Q: How does a two-colour pyrometer eliminate emissivity error? A: It compares radiance at two wavelengths; for a grey body the emissivity factor appears in both and cancels in the ratio, which also makes it tolerant to dust, smoke and a partially blocked view.
• Q: Why does a thermistor give high sensitivity but limited use in industry? A: Its resistance varies exponentially, giving several percent change per degree, but the same exponential makes the usable span narrow and strongly non-linear, and the devices are less interchangeable and less stable at high temperature than platinum.

Common mistakes

• Writing the thermocouple reading as the absolute hot-junction temperature and forgetting to add the cold-junction emf (or adding the ambient temperature in °C to the emf in mV).
• Using the linear R₀(1 + αt) form over a wide span and ignoring the Callendar–Van Dusen quadratic term, which costs several degrees above 200 °C.
• Mixing kelvin and Celsius in radiation problems — Stefan–Boltzmann and Wien need absolute temperature, and T⁴ makes the error huge.
• Assuming ε = 1 for a metal surface, or leaving the IR thermometer's emissivity on its default value.
• Connecting a 2-wire RTD on a long field run, or unequal/mismatched lead lengths on a 3-wire RTD, so the compensation does not cancel.
• Immersing the sensor too shallow in the thermowell or leaving an air gap, giving stem conduction error and a sluggish, low reading.
• Calling a temperature *difference* in °F or °R equal to the same number in °C or K (1 °C = 1 K but 1 °C = 1.8 °F of interval).

Related topics

• Transducers and sensors basics · Pressure measurement · Signal conditioning and 4–20 mA transmitters · Process control loops and PID tuning · Heat transfer: conduction, convection and radiation · Instrument calibration and NABL traceability.