🌡️ Thermal & Data Acquisition

Temperature is the one quantity on the bench that you almost never measure directly. You measure a voltage, a resistance, or a stream of infrared photons, and then you infer a temperature from it. Every link in that chain has an assumption baked in, and the whole craft of thermal data acquisition is keeping those assumptions honest and then recording everything in an order you can replay later. The throughline of this lesson is simple: pick the right sensor for the job, set the one knob that sensor demands, and log temperature alongside current and position so cause and effect line up on the same clock.

By the end, you can

1. Choose between a thermocouple, RTD, and thermistor for a given range, accuracy, and cost
2. Explain why a thermocouple needs cold-junction compensation and what happens if you skip it
3. Set the emissivity on an IR camera and predict the error when a shiny part is read at the wrong value
4. Design a multi-channel DAQ log that ties current, position, and temperature to one timebase
5. Relate thermal rise versus duty cycle to a motor's continuous-versus-peak torque limit

Intuition first

Think of the four temperature sensors as four different kinds of witnesses to the same event, each reliable in its own way and each with a tell.

The thermocouple is the witness who only reports differences. Join two unlike metals and a temperature gap along the wire produces a tiny voltage. It will happily tell you “the hot end is so many degrees above the cold end,” but it genuinely does not know how warm the cold end is, so you have to measure that separately. In exchange it covers an enormous range and needs no battery.

The RTD is the careful, slow witness. It is a coil or film of pure platinum whose resistance climbs in a clean, nearly straight line as it warms. Ask it the same question twice a year apart and you get the same answer, which is why laboratories lean on it. It costs more and reacts more slowly than the others.

The thermistor is the excitable witness. It is a bead of semiconducting oxide whose resistance plunges with heat, so a fraction of a degree moves the reading a lot. That sensitivity is wonderful near room temperature and useless far from it, because the response curves so hard it stops being readable. It is also the cheapest part in the drawer.

The IR camera is the witness across the room who never touches anything. It reads the infrared glow every warm surface gives off. The catch is that “how brightly a surface glows for its temperature” is a property called emissivity, and it varies wildly between a black plastic body (glows almost perfectly) and a polished metal tab (barely glows, mostly mirrors its surroundings). Tell the camera the wrong emissivity and it converts the right photons into the wrong temperature.

The deep idea behind all of them: none of these measures temperature. Each measures a proxy, and a proxy is only as good as the one assumption you feed it.

The contact sensors: voltage, resistance, and a curve

Thermocouple: the Seebeck voltage

Bond two dissimilar conductors and a temperature gradient along them drives a small voltage. This is the Seebeck effect, discovered in 1821, and the voltage is generated in the wire where the temperature changes, not at the junction itself (a point people get wrong constantly). The signal is tiny, in the microvolt range. A common Type K thermocouple gives roughly $41\ \mu\text{V}$ per degree Celsius, so a $100\ ^\circ\text{C}$ rise is only about four millivolts. That is why a thermocouple front-end is mostly a low-offset amplifier.

The voltage tells you the difference between the sensing (hot) junction and the reference (cold) junction where the wires meet your copper instrument. To turn that difference into an absolute temperature you must know the cold junction’s temperature, and then solve

$$E(T_\text{sense}) = V + E(T_\text{ref})$$

where $E(T)$ is the type’s tabulated voltage curve. Measuring $T_\text{ref}$ and correcting for it is called cold-junction compensation, usually done with a small semiconductor temperature sensor sitting right on the connector block. Skip it, assume the block is at a comfortable $25\ ^\circ\text{C}$ when it is really at $35\ ^\circ\text{C}$ because it is bolted next to a warm regulator, and every reading is off by that ten-degree mistake.

Thermocouples shine where nothing else survives: kiln walls, engine exhaust, furnace interiors, anywhere from cryogenic cold up past a thousand degrees. They are cheap, rugged, self-powered, and interchangeable. What they are not is accurate in the easy way. Getting system error below a single degree is hard, so they are the wrong tool for the gentle, high-precision job of, say, holding a chemistry bath at $37.0\ ^\circ\text{C}$.

RTD: platinum that keeps its word

A resistance temperature detector is a length of fine platinum wire (or a thin platinum film) whose resistance rises with temperature in a nearly linear way. The industry standard is the Pt100: exactly $100\ \Omega$ at $0\ ^\circ\text{C}$, climbing about $0.385\ \Omega$ per degree. Because the relationship is so stable and so close to a straight line, an RTD beats a thermocouple on accuracy and on repeatability, meaning it gives the same reading for the same temperature years apart with very little drift. Below about $600\ ^\circ\text{C}$ it is quietly replacing thermocouples in industry for exactly that reason.

The price you pay is real. Platinum costs money, the part responds more slowly than a thin thermocouple, and because you read it by passing a current through a small resistance, the resistance of your lead wires adds to the reading. The standard fix is a three-wire or four-wire connection that cancels the lead resistance out, a trick worth remembering when you wire one up.

The curve is not perfectly straight, and the precise form is the Callendar-Van Dusen equation,

$$R_T = R_0 \left[ 1 + A\,T + B\,T^2 \right] \quad (0\ ^\circ\text{C} \le T \lt 850\ ^\circ\text{C})$$

with $A = 3.9083 \times 10^{-3}\ ^\circ\text{C}^{-1}$ and $B = -5.775 \times 10^{-7}\ ^\circ\text{C}^{-2}$ for a standard platinum RTD. Because $B$ is so small, the quadratic term barely bends the line over a normal range, which is the whole reason RTDs feel linear.

Thermistor: cheap and exquisitely touchy

A thermistor is a bead of semiconducting metal oxide. The common kind is NTC, negative temperature coefficient: heat frees more charge carriers, so resistance falls as temperature rises, and it falls hard. Near room temperature a small NTC can change by thousands of ohms over a handful of degrees, which makes it trivial to read with a simple voltage divider and an ADC (your work in lessons #3 and #10 is exactly the front-end a thermistor wants).

That sensitivity is also its limit. The resistance drops so steeply that the useful window is narrow, typically something like $-90$ to $130\ ^\circ\text{C}$, and the curve is sharply nonlinear, so you cannot just scale it like a thermocouple. The honest model is the Steinhart-Hart equation,

$$\frac{1}{T} = a + b\,\ln R + c\,(\ln R)^3$$

a third-order fit in the log of resistance whose three constants come from calibrating the specific part. Feed it ohms and out comes absolute temperature to better than a few hundredths of a degree across a couple hundred degrees of range. For a robot hand monitoring a motor or a battery pack near human temperatures, a thermistor is often the right answer: pennies, fast, sensitive, and accurate enough once you store its curve.

The non-contact sensor: emissivity is the knob

An infrared camera or a pyrometer measures temperature without touching anything. It collects the infrared radiation a surface emits and works backward to a temperature using the Stefan-Boltzmann picture of how hot things glow. The radiated power per unit area from a real surface is

$$M = \varepsilon\,\sigma\,T^4$$

where $\sigma = 5.67 \times 10^{-8}\ \text{W}\,\text{m}^{-2}\,\text{K}^{-4}$ and $\varepsilon$ is emissivity, the fraction of an ideal black body’s glow that this particular surface actually puts out. Emissivity runs from 0 to 1. Matte black paint, plastic, oxidized metal, and human skin all sit high, around 0.9 to 0.97, close to a perfect emitter. Polished and shiny metals sit shockingly low: polished aluminium is about 0.04, polished copper about 0.04, polished silver about 0.02. A bright metal surface barely emits at all, and instead acts like a mirror that reflects the room back at the camera.

Here is the trap that opened this lesson. Most IR cameras default to an emissivity near 0.95, perfect for the painted and plastic surfaces that make up most of the world. Point that default at a shiny metal heatsink tab and the camera sees only the feeble glow the metal actually emits, assumes it came from a near-perfect emitter, and concludes the surface must be much colder than it is. The classic demonstration is a thermal photo of a cold beer can: the painted side reads one temperature, the bare aluminium end reads another entirely, and the polished metal even shows a ghostly reflection of a warm hand, all on a can that is uniformly one temperature. You must set the emissivity to match the surface, or paint a patch of known-emissivity matte tape on the shiny part and aim there.

   IR CAMERA reads the SAME real surface at 80 C, three ways:

   emissivity set to:   0.95          0.30          0.95 + matte tape
                         |             |             |
   shiny metal tab  -->  [ 41 C ]      [ 78 C ]      [ 80 C ]
                         too cold!     closer        correct
                         (default,     (set to the   (tape gives a
                          wrong knob)   metal's eps)  high-eps spot)

Data acquisition: log the whole story on one clock

A single sensor reading is a fact. A correlated log is an explanation. The point of a data acquisition (DAQ) system is to sample several channels at a defined, known sample rate and stamp them against one shared timebase, so that when the robot finger stalls you can lay current, joint position, and motor temperature on top of each other and read the story left to right.

The discipline has three parts. Channels: decide what you record. For the hand that is at least the motor current (lesson #27), the encoder position, and the driver temperature, plus the bus voltage if you have a spare channel. Sample rate: pick it deliberately. Temperature changes slowly, so a few samples per second is plenty for the thermistor, but current can spike in milliseconds, so it wants a far faster channel. Logging everything at the slow rate hides the current spike that caused the heat; logging everything at the fast rate floods your storage with redundant temperature points. Timebase: every sample carries the same clock so the columns line up. Without a shared clock you have three lists of numbers and no way to say which current spike produced which thermal rise.

When you get this right you can answer the question that matters: what did the hand do just before it got hot? That is causation you can see, not a guess. Your serial logging skills from lesson #12 are the cheap version of this; a real DAQ is the same idea with several synchronized channels and a sample clock you trust.

?An IR camera set to its default emissivity of 0.95 reads a polished copper motor tab as 38 °C, while a thermistor taped to the same tab reads 79 °C. What is the most likely explanation?

• A The thermistor is self-heating and reading high
• B Polished copper has very low emissivity (~0.04), so at ε = 0.95 the camera badly underreads the metal's temperature
• C The thermocouple cold junction was not compensated
• D Copper conducts heat so well that its surface is genuinely cooler than the inside

?You need to hold a small chemistry bath at 37.0 °C and read it to within 0.1 °C near room temperature, at the lowest cost. Which sensor fits best?

• A A Type K thermocouple, because it covers the widest range
• B An NTC thermistor, because it is cheap and extremely sensitive near room temperature
• C An IR camera, because it needs no contact with the liquid
• D Any of them (the choice does not affect accuracy)

Lab: a three-channel thermal capture of one finger

On the bench, instrument one finger driver. Tape a small NTC thermistor flat to the driver IC’s heat tab with a dab of thermal compound, and read it through a voltage divider into an ADC channel, converting ohms to degrees with the part’s stored Steinhart-Hart constants. Bring the motor current onto a fast channel from your lesson #27 shunt, and the encoder count onto a third. Log all three to one timebase at, say, $2\ \text{kHz}$ for current and position and $5\ \text{Hz}$ for temperature, then drive the finger through a repeating grip-and-release at a fixed duty cycle. Plot the three traces stacked on the same time axis. You should see the thermal rise lag the current, settle toward a steady value, and tell you what duty cycle the driver can sustain forever versus what it can only do in short bursts. While you are there, point an IR camera at the same tab twice, once at the default emissivity and once set for bare metal, and watch the reading jump.

↘ Why a polished beer can shows three temperatures, and the math of CJC

Two ideas from the grounding deserve a closer look. First, why appearance fools you. Emissivity is tied by Kirchhoff’s law of thermal radiation to a surface’s ability to absorb: a good absorber at a given wavelength is an equally good emitter at that wavelength. At the ten-micrometre infrared wavelengths a room-temperature camera works in, matte paint (even white paint), plastic, skin, and oxidized metal are excellent absorbers and so emit with emissivity around 0.9 to 0.97. Bare polished metal absorbs almost nothing in the infrared, reflects nearly everything, and so emits feebly, with emissivity as low as 0.02 for silver. That is why the famous thermograph of a cold beer can shows wildly different apparent temperatures across one uniform-temperature object, and why a polished face even shows a reflection of a warm hand. The radiated power follows $M = \varepsilon\,\sigma\,T^4$, so if the true surface is at temperature $T$ but the camera assumes $\varepsilon = 1$ when the metal’s real value is $\varepsilon_\text{real}$, the apparent temperature it reports satisfies $T_\text{app}^4 \approx \varepsilon_\text{real}\,T^4$, giving $T_\text{app} \approx \varepsilon_\text{real}^{1/4}\,T$. For polished copper ($\varepsilon_\text{real} \approx 0.04$) that fourth-root factor is about 0.45, so a true $353\ \text{K}$ ($80\ ^\circ\text{C}$) surface masquerades as roughly $159\ \text{K}$ of apparent contribution before reflected room radiation muddies it further. The number is approximate because reflected background and the camera’s own model complicate it, but the direction is unmistakable: shiny metal always reads far too cold.

Second, the structure of cold-junction compensation. A thermocouple obeys $V = E(T_\text{sense}) - E(T_\text{ref})$, where $E(T)$ is the type’s characteristic curve (Type K, chromel-alumel, is the usual general-purpose choice). The meter’s copper terminals are the reference junction, and a separate semiconductor sensor measures $T_\text{ref}$ there. The instrument then computes $V + E(T_\text{ref})$ and searches the $E(T)$ table for the temperature whose curve value matches, recovering $T_\text{sense}$. Because $E(T)$ is itself nonlinear, an error in $T_\text{ref}$ does not map to an equal error in $T_\text{sense}$; some types, like Type B, have a nearly flat curve near room temperature precisely so a sloppy reference barely matters. The historical alternative was an ice bath holding the reference at a hard $0\ ^\circ\text{C}$ by the physics of melting water, which is why the very best thermocouple references are still ice points.

Grounded in Wikipedia: “Thermocouple”, “Resistance thermometer”, “Thermistor”, “Emissivity” (CC BY-SA).

Key takeaways

• ▸None of these sensors measures temperature directly. A thermocouple measures a Seebeck voltage, an RTD and thermistor measure resistance, an IR camera measures radiated infrared. Each infers temperature from a proxy with one critical assumption.
• ▸Thermocouple = wide range, self-powered, but needs cold-junction compensation; skip the reference-junction measurement and every reading is off by the cold junction's true offset.
• ▸RTD = platinum, accurate and nearly linear and repeatable below ~600 °C; thermistor = cheap and extremely sensitive but narrow and nonlinear, best near room temperature.
• ▸IR cameras demand the emissivity knob: a shiny metal part (ε ≈ 0.04) read at the default ε ≈ 0.95 reports far too cold. Set ε, or aim at a matte-tape patch.
• ▸A DAQ log on one timebase turns readings into explanation: current, position, and temperature on a shared clock let you see cause and effect, not guess at it.
• ▸Thermal rise versus duty cycle sets the continuous-versus-peak torque limit of a motor. The temperature trace is what tells you what the actuator can do forever versus only in bursts.

Practice 1 warm-up

For each job, name the best of thermocouple / RTD / thermistor and say why in one line: (a) monitor a gas-turbine exhaust at $900\ ^\circ\text{C}$; (b) hold a laboratory reference bath and read it to $0.05\ ^\circ\text{C}$ near $25\ ^\circ\text{C}$; (c) cheaply watch a battery pack’s temperature on a robot hand near body temperature.

↘ Show worked solution

(a) Thermocouple. Only it survives $900\ ^\circ\text{C}$ comfortably; an RTD is usually limited to about $600\ ^\circ\text{C}$ in industry and a thermistor’s useful window ends far below that. Wide range and ruggedness win.

(b) RTD (Pt100). Near room temperature you want the most accurate, lowest-drift, most repeatable sensor, and platinum RTDs are the laboratory standard for exactly this. A thermistor could hit the resolution but the RTD wins on long-term stability for a reference.

(c) Thermistor. Cheap, fast, and extremely sensitive right around body temperature, with sub-tenth-degree accuracy once its curve is stored, and it reads straight into an ADC through a divider. Range and stability do not matter here; cost and sensitivity do.

Practice 2 core

A bench IR camera left at its default emissivity of $0.95$ reads a polished aluminium heatsink (true emissivity about $0.05$) as suspiciously cool. Using the rough relation $T_\text{app} \approx \varepsilon_\text{real}^{1/4}\,T$ (true temperature $T$ in kelvin, ignoring reflected background), estimate the apparent temperature the camera shows when the heatsink is truly at $90\ ^\circ\text{C}$. Then state the two practical fixes.

↘ Show worked solution

Convert to kelvin: $T = 90 + 273 = 363\ \text{K}$. The fourth root of the true emissivity is $\varepsilon_\text{real}^{1/4} = 0.05^{1/4}$. Since $0.05^{1/2} \approx 0.224$ and $0.224^{1/2} \approx 0.473$, we get $T_\text{app} \approx 0.473 \times 363 \approx 172\ \text{K}$, which is about $-101\ ^\circ\text{C}$. The camera would show the hot heatsink as wildly, impossibly cold, the unmistakable signature of an emissivity mismatch on bare metal. (The real reading is warmer than this because reflected room radiation adds in, but it is still far below the true $90\ ^\circ\text{C}$.) The two fixes: set the camera’s emissivity to the metal’s real value (about $0.05$), or stick a patch of matte high-emissivity tape on the surface and aim at the patch, reading a known $\varepsilon \approx 0.95$ spot.

Practice 3 stretch

You log motor current and driver temperature on one timebase while running a finger at three duty cycles. At 30 percent duty the tab settles at $45\ ^\circ\text{C}$; at 60 percent it settles at $72\ ^\circ\text{C}$; at 100 percent the temperature never settles and climbs past the driver’s $125\ ^\circ\text{C}$ rating. The room is at $25\ ^\circ\text{C}$. Treat the steady temperature rise above ambient as roughly proportional to the average power dissipated, and the power as roughly proportional to duty cycle. Estimate the highest duty cycle the driver can run continuously without exceeding $125\ ^\circ\text{C}$, and explain what this has to do with continuous-versus-peak torque.

↘ Show worked solution

Work in temperature rise above the $25\ ^\circ\text{C}$ room. At 30 percent duty the rise is $45 - 25 = 20\ ^\circ\text{C}$; at 60 percent it is $72 - 25 = 47\ ^\circ\text{C}$. Both are consistent with rise being roughly proportional to duty: doubling the duty from 30 to 60 percent roughly doubles the rise ($20$ to $47$, close enough given a real system). Take the slope as about $47 / 60 \approx 0.78\ ^\circ\text{C}$ of rise per percent of duty (the 30-percent point gives a similar $20 / 30 \approx 0.67$; call it roughly $0.7\text{–}0.8$). The allowed rise is $125 - 25 = 100\ ^\circ\text{C}$. So the sustainable duty is about $100 / 0.78 \approx 128$ percent by the linear fit, but duty cannot exceed 100 percent, and the data already shows 100 percent never settles, so the simple proportional model is optimistic at the top end (thermal resistance and reduced cooling margin bend the curve up). The honest reading: the driver can run continuously somewhere in the 70 to 85 percent duty band with margin below $125\ ^\circ\text{C}$, and 100 percent is a peak-only burst. That gap is exactly the continuous-versus-peak torque limit: torque tracks current tracks duty, so the duty the driver can hold forever without cooking sets the continuous torque, while the higher duty it can survive only briefly sets the peak torque. The thermal log, not the datasheet alone, is what draws that line for your specific mounting and airflow.