Temperature and Analytical Measurement

Temperature Measurement and Analysis

Introduction

Temperature measurement and fluid analysis are two fundamental areas of the instrumentation and control technician trade. On the Red Seal exam, these topics represent a significant portion of the questions, both theoretical and practical. This chapter covers the physical principles, types of instruments, calibration calculations, applicable Canadian standards, and common pitfalls to avoid.

Temperature is the most measured physical quantity in industrial processes — approximately 50% of measurement points in a typical plant. Chemical analysis (pH, conductivity, humidity, gas composition) complements this measurement to ensure product quality and facility safety.

Fundamental Principles of Temperature Measurement

Temperature Scales and Conversions

Three scales are used in industrial instrumentation: Celsius (°C), Fahrenheit (°F), and Kelvin (K). The Rankine scale (°R) is rarely encountered in Canada but may appear in American equipment documentation.

Essential conversion formulas:

°F = (°C × 9/5) + 32

°C = (°F − 32) × 5/9

K = °C + 273.15

°R = °F + 459.67

Quick reference table:

Reference point	°C	°F	K
Absolute zero	−273.15	−459.67	0
Freezing point of water	0	32	273.15
Boiling point of water (1 atm)	100	212	373.15
Typical ambient temperature	20	68	293.15

> Exam tip: To quickly convert °C to °F, double the °C value and add 30. This mental calculation gives a sufficient approximation to check the plausibility of a result.

Zeroth Law of Thermodynamics

Temperature measurement is based on the zeroth law of thermodynamics: if two bodies are each in thermal equilibrium with a third, they are in thermal equilibrium with each other. The measuring instrument must reach thermal equilibrium with the process to indicate the true temperature. This concept explains a sensor's response time — a massive sensor responds more slowly than a low-mass sensor.

Types of Temperature Sensors

Expansion Thermometers

Liquid-in-glass thermometers: Use the differential expansion of mercury (banned in Canada for food applications) or a colored liquid (alcohol, toluene). Accuracy of ±0.5 °C to ±2 °C depending on the range.

Liquid expansion thermometers (bulb type): A bulb filled with liquid (often mercury or an organic fluid) connected to a capillary tube and a measuring element (Bourdon tube). The liquid pressure increases with temperature. Used in ranges from −40 °C to +650 °C.

Vapor pressure thermometers: The bulb contains a volatile liquid that is partially vaporized. The saturated vapor pressure depends only on temperature. Typical ranges: −40 °C to +300 °C.

Bimetallic thermometers: Two metals with different expansion coefficients (often invar and brass) are bonded together. The deformation of the spiral or ribbon drives the pointer. Accuracy of ±1% of full scale. Used for local indication, never for signal transmission.

Resistance Temperature Detectors (RTDs)

The RTD (Resistance Temperature Detector) exploits the variation of electrical resistance of a pure metal with temperature. Platinum is the standard metal because its resistance-temperature relationship is stable and repeatable.

Platinum characteristics:

Temperature coefficient α = 0.00385 Ω/Ω/°C (IEC 60751 standard)

Callendar-Van Dusen equation for the range −200 °C to +850 °C

Excellent linearity compared to thermocouples

Simplified equation for 0 °C to 850 °C:

R(T) = R₀ × (1 + αT)

Where R₀ = 100 Ω for a PT100, 1000 Ω for a PT1000.

Calculation example: A PT100 at 150 °C has a resistance of:

R = 100 × (1 + 0.00385 × 150) = 100 × (1 + 0.5775) = 100 × 1.5775 = 157.75 Ω

2, 3, and 4-wire connections:

Type	Advantages	Disadvantages
2-wire	Simple, economical	Error due to lead wire resistance (uncompensated)
3-wire	Compensates for lead wire resistance	Requires 3 conductors
4-wire	Most accurate measurement (Kelvin method)	Higher cost, 4 conductors

> Exam trap: The 2-wire connection is acceptable for short distances and low accuracy requirements. For accuracy better than ±0.5 °C, a 3 or 4-wire connection is mandatory.

Thermocouples

A thermocouple consists of two different metals welded together at one end (measuring junction). The other end (reference junction) is maintained at a known temperature. The voltage generated (Seebeck effect) is proportional to the temperature difference between the two junctions.

Standardized types (IEC 60584):

Type	Metals	Useful range (°C)	Sensitivity (µV/°C)	Typical application
J	Iron / Constantan	0 to 750	52	General processes
K	Chromel / Alumel	−200 to 1250	41	Furnace, heat treatment
T	Copper / Constantan	−200 to 350	43	Low temperatures
E	Chromel / Constantan	−200 to 900	68	High sensitivity
S	Platinum 10% Rh / Platinum	0 to 1450	10	High temperature, standards
R	Platinum 13% Rh / Platinum	0 to 1450	11	High temperature
B	Platinum 30% Rh / Platinum 6% Rh	200 to 1700	5	Very high temperature

Law of intermediate metals: Inserting a third metal into the circuit does not change the total voltage if the two junctions formed are at the same temperature. This law justifies the use of terminal blocks and copper connection wires.

Cold junction compensation: The measured voltage depends on the reference junction temperature. Modern transmitters measure this temperature with an internal RTD and compensate automatically. Compensation is essential for accuracy.

> Exam tip: Type K is the most common in industry. Type T is preferred for low temperatures. Type B does not require cold junction compensation because its voltage is zero at 0 °C.

Optical and Infrared Pyrometers

Infrared pyrometers measure temperature without contact by detecting the thermal radiation emitted by a surface. They are used for:

Moving objects (conveyor belts, rotating parts)

Hazardous or inaccessible environments

Very high temperatures (> 1000 °C)

Factors affecting accuracy:

Emissivity (ε) of the surface: varies from 0.05 (polished metal) to 0.95 (flat black surface). Incorrect emissivity causes significant errors.

Measurement distance (distance-to-spot-size ratio)

Atmospheric interference (vapor, dust)

Viewing angle (perpendicular to the surface is ideal)

Stefan-Boltzmann law: P = ε × σ × T⁴, where σ = 5.67 × 10⁻⁸ W/m²·K⁴. The radiated power increases with the fourth power of absolute temperature — this is why pyrometers are very sensitive at high temperatures.

Temperature Transmitters

Typical Configuration

A temperature transmitter converts the sensor signal (resistance or millivolts) into a standardized output signal: 4-20 mA, HART, Foundation Fieldbus, or Profibus PA.

Configuration steps:

63.Select the sensor type (RTD PT100, type K thermocouple, etc.)

64.Configure the measurement range (0 to 200 °C, for example)

65.Set cold junction compensation (for thermocouples)

66.Configure the fault alarm (high or low)

67.Loop test (verify the 4-20 mA signal)

Transmitter Calibration

Two-point calibration:

70.Apply the low range temperature (e.g., 0 °C with an ice bath)

71.Adjust the zero (offset) to obtain 4 mA at the output

72.Apply the high range temperature (e.g., 100 °C with a boiling water bath)

73.Adjust the gain (span) to obtain 20 mA at the output

74.Repeat steps 1 to 4 until convergence

Error calculation:

Error (%) = [(Measured value − True value) / Full scale] × 100

Example: A transmitter configured for 0-200 °C indicates 102 °C when the true temperature is 100 °C.

Error = [(102 − 100) / 200] × 100 = 1% of full scale

> Exam trap: Error is always expressed as a percentage of full scale, not as a percentage of the reading. An error of 2 °C on a 0-200 °C range represents 1%, but on a 0-100 °C range, it represents 2%.

Analytical Measurement Principles

pH Measurement

pH measures the activity of hydrogen ions in a solution: pH = −log₁₀[H⁺]. The scale ranges from 0 (acidic) to 14 (basic), with 7 as the neutral point at 25 °C.

Glass electrode: The measuring electrode contains an internal buffer solution and a glass membrane sensitive to H⁺ ions. The reference electrode (calomel or Ag/AgCl) provides a stable potential. The potential difference between the two electrodes is proportional to pH.

Nernst equation:

E = E₀ + (2.303 × R × T / n × F) × log₁₀[H⁺]

Where R = 8.314 J/mol·K, F = 96485 C/mol, n = 1 for H⁺.

At 25 °C, the theoretical slope is 59.16 mV per pH unit.

pH meter calibration:

90.Two-point calibration with buffer solutions (pH 4.00 and 7.00, or pH 7.00 and 10.00)

91.Rinse the electrode with deionized water between buffers

92.Check the slope (must be between 90% and 105% of the theoretical slope)

93.Check the offset — should be close to 0 mV

Factors affecting the measurement:

Temperature: The pH of a solution varies with temperature. Automatic compensation is necessary for significant variations.

Dirty or fouled electrode: Causes slow and unstable readings.

Dehydrated electrode: Must be rehydrated in a 3 M KCl solution.

Junction potential: Clogging of the reference junction causes errors.

> Exam tip: Temperature affects both the pH of the solution AND the electrode slope. Temperature compensation corrects the slope, but does not correct the actual change in the solution's pH.

Conductivity

Conductivity measures a solution's ability to conduct electrical current. It depends on the ion concentration, their mobility, and temperature.

Unit: Siemens per meter (S/m) or microsiemens per centimeter (µS/cm). Ultrapure water has a conductivity of approximately 0.055 µS/cm; seawater approximately 50,000 µS/cm.

Conductivity cell: Two electrodes of known surface area, separated by a known distance. The cell constant (K) is the distance-to-surface ratio, typically 0.1, 1.0, or 10 cm⁻¹.

Conductivity calculation:

G = K / R

Where G is the conductance (S), K the cell constant (cm⁻¹), R the measured resistance (Ω).

Example: A cell with K = 1.0 cm⁻¹ measures a resistance of 2000 Ω.

G = 1.0 / 2000 = 0.0005 S = 500 µS/cm

Temperature compensation: Conductivity increases by approximately 2% per °C. The standard compensation is 2.1%/°C, referenced to 25 °C.

Corrected conductivity:

G₂₅ = G_T / [1 + α × (T − 25)]

Where α = 0.021 (temperature coefficient), T in °C.

> Exam trap: Temperature compensation is a mathematical correction. It does not change the actual conductivity of the solution — it brings it back to a reference value at 25 °C for comparison.

Dissolved Oxygen Analysis

Dissolved oxygen (DO) measurement is critical in boilers, water treatment plants, and the food and beverage industry.

Methods:

Electrochemical method (Clark cell): An oxygen-permeable membrane separates the electrolyte from the solution. Oxygen diffuses through the membrane and is reduced at the cathode, generating a current proportional to the concentration.

Optical method (luminescence): A fluorescent compound is excited by pulsed light. The presence of oxygen quenches the fluorescence; the decay time is inversely proportional to the O₂ concentration.

Units: mg/L (ppm) or % saturation. At 25 °C and 1 atm, saturation is approximately 8.26 mg/L in fresh water.

Factors affecting the measurement:

Temperature (O₂ solubility decreases with temperature)

Barometric pressure (solubility increases with pressure)

Salinity (solubility decreases with salinity)

Solution flow rate (minimum 0.3 m/s for electrochemical cells)

Humidity Analysis

Relative humidity (% RH) is the ratio of the partial pressure of water vapor in air to the saturated vapor pressure at the same temperature, expressed as a percentage.

Instruments:

Psychrometer: Two thermometers (dry bulb and wet bulb). The temperature difference indicates humidity via psychrometric tables.

Capacitive sensor: A hygroscopic polymer whose dielectric constant varies with humidity. The most common in industry.

Resistive sensor: A hygroscopic salt whose resistance varies with humidity.

Dew point: The temperature at which air becomes saturated. Measured by a chilled mirror (optical method) or a capacitive sensor.

Pressure dew point: For compressed gases, the pressure dew point is higher than the atmospheric dew point. Conversion requires the system's absolute pressure.

Canadian Standards and Codes

Canadian Electrical Code, Part I, Chapter V

The Canadian Electrical Code, Part I, Chapter V (CE Code, Chapter V) governs the installation of electrical equipment in classified areas (hazardous locations). Temperature and analysis instruments installed in these areas must be certified in accordance with the requirements.

Rule 18-006: Classification of locations — areas are classified according to the nature of the hazardous materials present (Class I: gases and vapors; Class II: dusts; Class III: fibers).

Rule 18-100: General requirements for the installation of equipment in Class I locations.

Rule 18-150: Protection methods — instruments may be certified for:

Explosion-proof

Intrinsic safety (IS) — the most common method for measuring instruments

Encapsulation

Pressurized enclosure (purging)

Rule 18-302: Requirements for intrinsically safe circuits — intrinsic safety barriers (Zener or galvanic) must be installed outside the hazardous area.

> Exam tip: Intrinsic safety is the preferred method for measuring instruments because it limits the available energy to a level incapable of igniting the hazardous atmosphere. Zener barriers must be grounded (Rule 18-302).

CSA B149.1 — Natural Gas and Propane Code

CSA B149.1 applies to the installation of natural gas and propane appliances. Temperature measurement and analysis instruments installed on gas lines or burners must comply with:

Article 5.4: Requirements for combustion control systems — temperature limits and safety interlocks.

Article 6.18: Requirements for gas leak detectors and combustion analyzers.

Article 7.22: Requirements for ventilation systems and carbon monoxide detectors.

CSA C22.2 — Safety Standards for Electrical Equipment

Instruments sold in Canada must be certified to CSA C22.2 standards (e.g., CSA C22.2 No. 142 for process transmitters). This certification is mandatory for installation in Canadian industrial facilities.

Installation and Commissioning Procedures

Temperature Sensor Installation

Thermowells:

Protect the sensor from the process (pressure, corrosion, erosion)

Increase response time (the air between the well and the sensor is an insulator)

Must be filled with a thermally conductive material (thermal paste, oil) to improve heat transfer

Insertion length: minimum 10 well diameters into the fluid

Measurement location:

The sensor must be immersed in the fluid, not in a dead zone

Avoid stagnation areas, elbows, and low points where gas pockets can form

For gases: install vertically or inclined to prevent condensate accumulation

For liquids: install horizontally or inclined to prevent vapor pockets

Loop Verification

Complete verification procedure:

168.Verify the power supply (24 VDC typical for a 4-20 mA transmitter)

169.Verify wire continuity and connections (tight terminal blocks, correct polarity)

170.Simulate the sensor with a thermocouple simulator or a resistance box (for RTD)

171.Verify the output signal at the transmitter (4 mA at zero, 20 mA at maximum)

172.Verify the signal at the control room (reading at the DCS/SCADA system)

173.Document the results in the commissioning report

Loop test with a calibrator:

A temperature calibrator simulates the sensor (RTD or thermocouple)

A loop calibrator measures the 4-20 mA current

The total loop accuracy must be verified from end to end

Practical Calculations and Conversions

Measurement Range Calculation

Example: An RTD PT100 transmitter is configured for a range of 0 to 150 °C. What is the resistance at mid-scale?

R₀ = 100 Ω, α = 0.00385 Ω/Ω/°C

R(75 °C) = 100 × (1 + 0.00385 × 75) = 100 × 1.28875 = 128.875 Ω

The output signal at mid-scale: 4 + (20 − 4) × 0.5 = 12 mA

Transmitter Output Calculation

General formula:

I_output = 4 + (16 × (T_measured − T_min) / (T_max − T_min))

Example: Transmitter configured for 0-200 °C. What is the output at 80 °C?

I = 4 + (16 × (80 − 0) / (200 − 0)) = 4 + (16 × 0.4) = 4 + 6.4 = 10.4 mA

Reverse Calculation — Determining Temperature from Current

Example: The measured signal is 14 mA. What is the temperature?

T = T_min + [(I − 4) / 16] × (T_max − T_min)

T = 0 + [(14 − 4) / 16] × 200 = (10/16) × 200 = 125 °C

Thermocouple Conversion — Reference Table

For a type K thermocouple, the voltage at 100 °C is approximately 4.096 mV (reference junction at 0 °C). The relationship is non-linear; standardized tables (IEC 60584) are used for precise conversions.

Pitfalls to Avoid

198.Confusing the sensor type: An RTD measures resistance (Ω), a thermocouple measures voltage (mV). Never connect an RTD to a thermocouple input or vice versa.

199.Forgetting cold junction compensation: For a thermocouple, if the reference junction is not compensated, each degree of ambient temperature variation introduces an error of approximately 41 µV (type K), or about 1 °C.

200.Neglecting lead wire resistance in 2-wire connections: For an RTD PT100, each ohm of lead wire resistance introduces approximately 2.6 °C of error. A 100 m run of 22 AWG wire (0.16 Ω/m) adds 16 Ω, or approximately 41 °C of error!

201.Using the wrong temperature coefficient: The coefficient α = 0.00385 is the IEC standard. Some American RTDs use α = 0.00392 (old standard). Confusion causes measurement errors.

202.Ignoring emissivity in pyrometry: Measuring a polished metal surface (ε = 0.1) with a pyrometer set for ε = 0.95 gives a falsely low reading of several hundred degrees.

203.Calibrating a pH meter with expired buffers: Buffer solutions have a limited shelf life. A contaminated or expired buffer gives a false calibration.

204.Forgetting temperature compensation in conductivity: Without compensation, a 10 °C variation causes an error of approximately 21% in the reading.

205.Installing a thermowell that is too short: A well insufficiently inserted into the fluid measures the wall temperature, not the process temperature.

206.Confusing the standards: CE Code Chapter V applies to hazardous locations; CSA B149.1 applies to natural gas and propane. Both may apply simultaneously to the same instrument.

207.Neglecting response time: A massive sensor in a thermowell can have a response time of several minutes. For process control, this delay can cause instability.

Summary

Temperature is measured by four major families: expansion (bimetallic, liquid), resistance (RTD), thermocouples, and radiation (pyrometers).

Platinum RTDs (PT100) offer the best accuracy and stability for the range −200 °C to +850 °C. A 3 or 4-wire connection is required for accuracy.

Thermocouples cover wider ranges but are less accurate. Type K is the most common; type B does not require cold junction compensation.

Cold junction compensation is essential for thermocouples. Modern transmitters incorporate it automatically.

Calibration is done at two points (zero and full scale). Error is expressed as a percentage of full scale.

pH is measured with a glass electrode. Two-point calibration with fresh buffers is mandatory. The slope must be verified.

Conductivity depends on ionic concentration and temperature. Compensation at 25 °C is standard.

Applicable Canadian standards: CE Code Chapter V (hazardous locations), CSA B149.1 (gas), CSA C22.2 (equipment safety).

4-20 mA loop calculations: I = 4 + 16 × (T − T_min) / (T_max − T_min). Master both direct and reverse conversions.

Review Questions

221.A type K thermocouple measures a voltage of 4.096 mV with a reference junction at 0 °C. What is the approximate temperature? (Answer: approximately 100 °C)

222.A PT100 RTD in a 2-wire connection with a total lead wire resistance of 5 Ω indicates a resistance of 130 Ω. What is the true temperature? (Answer: R_sensor = 130 − 5 = 125 Ω; T = (125/100 − 1) / 0.00385 = 64.9 °C)

223.A 4-20 mA transmitter is configured for 50 to 250 °C. The measured signal is 8 mA. What is the temperature? (Answer: T = 50 + [(8 − 4)/16] × 200 = 50 + 50 = 100 °C)

224.What is the main difference between an RTD and a thermocouple in terms of measurement principle? (Answer: The RTD measures a change in resistance; the thermocouple generates a voltage through the Seebeck effect.)

225.Why is the 4-wire connection the most accurate for an RTD? (Answer: It completely eliminates the effect of lead wire resistance by separating the excitation circuit from the measurement circuit — the Kelvin method.)

This chapter covers the essential knowledge required to succeed on the Red Seal exam questions on temperature measurement and analysis. Review the reference tables, practice the loop calculations, and memorize the applicable Canadian standards. Good luck with your preparation!