Calculate how much electromotive force a thermocouple of two dissimilar metal wires produces through the Seebeck effect. Adjust the hot- and cold-junction temperatures, the Seebeck coefficient and the amplifier gain to see the thermal EMF, cold-junction compensation voltage and amplified output update in real time.
Parameters
Measuring (hot) junction T_hot
°C
Junction placed on the object whose temperature you measure
Reference (cold) junction T_cold
°C
Junction at the terminal block / instrument, usually at room temperature
Seebeck coefficient S
µV/°C
Sensitivity set by the metal pair. Type K ~41, type E ~68, type R/S ~10
Instrumentation-amplifier gain G
×
Factor that raises the microvolt-level signal to volt level
Results
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Temp. difference ΔT (°C)
—
Thermal EMF (mV)
—
Cold-junction comp. (mV)
—
0 °C-referenced EMF (mV)
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Amplifier output (V)
—
Sensitivity rating
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Thermocouple circuit — EMF animation
Two dissimilar metal wires join at a hot (measuring) junction shown glowing and a cold (reference) junction, generating a Seebeck EMF. The charge flow and EMF reading scale with the temperature difference.
Thermal EMF vs hot-junction temperature
Amplifier output vs gain
Theory & Key Formulas
$$\text{EMF}=S\cdot(T_{hot}-T_{cold})$$
Thermal EMF. S is the Seebeck coefficient (sensitivity set by the metal pair), T_hot the hot junction and T_cold the cold junction temperature. The EMF is proportional to the temperature difference.
Cold-junction compensation voltage V_CJC and the 0 °C-referenced equivalent EMF. Cold-junction compensation refers the reading to a 0 °C baseline so standard thermocouple tables apply, and EMF_0 = EMF + V_CJC.
$$V_{out}=\text{EMF}\cdot G$$
Instrumentation-amplifier output voltage V_out. G is the amplifier gain, which raises the tiny microvolt-level Seebeck voltage to a usable volt-level signal.
What is the Thermocouple and the Seebeck Effect?
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A "thermocouple" — I hear that name a lot for factory temperature sensors, but isn't it just two thin metal wires? How can that measure temperature?
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Good question. Take two wires of different metals and join them at both ends to form a loop — that alone is a temperature sensor. It is a phenomenon discovered by Thomas Seebeck in 1821: when the two joints (junctions) are at different temperatures, a tiny voltage — an electromotive force, or EMF — appears in the circuit. Measure that voltage and you have a temperature.
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Wait — just joining metals produces a voltage? Why does that happen?
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Roughly speaking, in any conductor a temperature difference (a gradient) along the wire makes the electrons drift a little from the hot side to the cold side, producing a small voltage. But in a loop of a single metal, the same thing happens on both sides and cancels out to zero. With two different metals it does not fully cancel, and a net measurable voltage survives. That is the heart of the Seebeck effect.
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I see. When I raise "ΔT" on the left, the EMF climbs steadily. So is it set by the hot-junction temperature itself?
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That is the crucial — and most misunderstood — point. A thermocouple EMF is set not by the absolute temperature of the hot junction but by the temperature difference between the two junctions. So to know the temperature of the junction you care about, you must always know the temperature of the other one — the "cold" or reference junction. In the old days that junction was held in 0 °C ice water.
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Ice water! Surely nobody prepares ice for that anymore?
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Today an electronic circuit does it. A separate sensor (a thermistor, for example) measures the cold-junction temperature, and the matching EMF is added by calculation. That gives you "the voltage you would have seen if the cold junction had been at 0 °C". This is cold-junction compensation (CJC). The "cold-junction comp." and "0 °C-referenced EMF" in this tool are exactly that correction. Standard thermocouple tables are built for a 0 °C reference, so without this correction the temperature conversion is off.
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There is also an "amplifier output". Why bother amplifying it?
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Because the Seebeck voltage is just so small — only tens of microvolts per degree. Even a type K reaches just about 11 mV for a 275 °C difference. Feed that straight into an ADC and you do not have enough resolution. So an instrumentation amplifier with a gain of 100 to 1000 turns it into an easy-to-handle volt-level signal. The choice of metal pair matters too: type K is the 41 µV/°C workhorse, type E has the highest sensitivity and suits low temperatures, and types R, S and B have low sensitivity but survive temperatures around 1600 °C.
Frequently Asked Questions
In the linear approximation (treating the Seebeck coefficient as constant), the thermal EMF is EMF = S(T_hot - T_cold). S is the Seebeck coefficient in microvolts per degree Celsius, T_hot is the measuring (hot) junction temperature and T_cold is the reference (cold) junction temperature. The key point is that the EMF depends on the temperature difference between the two junctions, not on the absolute temperature of the hot junction alone. This tool reports the EMF in both microvolts and millivolts.
Because a thermocouple EMF depends on a temperature difference, converting it to a temperature requires knowing the cold (reference) junction temperature. Standard thermocouple tables assume the cold junction sits at 0 C, so a separate sensor measures the actual cold-junction temperature and a compensation voltage S*T_cold is added to refer the reading back to a 0 C baseline. That is cold-junction compensation. This tool displays the compensation voltage in millivolts.
The Seebeck voltage of a thermocouple is very small, only tens of microvolts per degree, so it is hard to read directly with an ADC or a meter. A type-K thermocouple gives about 41 microvolts per degree, so even a 275 C difference produces only about 11 mV. An instrumentation amplifier with a gain of 100 to 1000 raises it to an easy-to-handle signal of a few volts. The amplifier output voltage in this tool, EMF times gain, is that amplified signal.
Choose by Seebeck coefficient (sensitivity) and temperature range. Type K has a moderate coefficient of about 41 microvolts per degree and a wide range of -200 to 1200 C, making it the most common workhorse. Type E has the highest coefficient at about 68 microvolts per degree and suits low-temperature work. The noble-metal types R, S and B have a low coefficient of about 10 microvolts per degree but survive temperatures around 1600 C. This tool estimates the rough equivalent type from the Seebeck coefficient.
Real-World Applications
Industrial furnaces and plant temperature measurement: Thermocouples are the most widely used temperature sensors in industry. Electric furnaces, boilers, heating ovens and gas-turbine exhaust temperatures — high-temperature measurement from a few hundred to over a thousand degrees almost always uses thermocouples. The wide range, fast response and low cost are the reasons; type K is the general-purpose choice, while noble-metal types R, S and B are picked for the highest temperatures. Vary the temperature difference and Seebeck coefficient in this tool to see intuitively how the EMF level differs between types.
Instrumentation circuits and data-logger design: Handling the tens-of-microvolts signal of a thermocouple makes the instrumentation amplifier and the cold-junction compensation circuit the heart of the design. The amplifier gain is chosen so that the thermocouple's maximum EMF fills the ADC full scale. The amplifier-output chart in this tool helps you judge where the output approaches saturation as the gain changes.
Cooking, kitchen and home appliances: Thermocouples also control the temperature in ovens, fryers and water heaters. A gas appliance's "flame-failure safety device" keeps the gas valve open only while the pilot flame keeps the thermocouple producing an EMF — a classic application of the Seebeck effect directly as a safety mechanism. When the flame goes out the EMF drops and the valve closes automatically.
Research and experimental measurement: Heat treatment of materials, tracking the temperature of chemical reactions, monitoring vacuum chambers and cryostats — thermocouples are a research-bench staple too. At cryogenic temperatures type E or type T is used, and at high temperatures the noble-metal types, choosing the type to match the temperature band. In calibration, managing the reference-junction temperature is the key to accuracy, so the cold-junction compensation concept of this tool maps directly to real practice.
Common Misconceptions and Pitfalls
The biggest misconception is assuming the thermocouple EMF is set by the hot-junction temperature itself. In reality the EMF is set by the temperature difference between the two junctions. You can confirm it in this tool: hold the hot junction fixed and raise the cold-junction temperature, and the EMF falls. So without knowing the cold (reference) junction temperature, no matter how accurately you measure the voltage you cannot convert it to a temperature. Skipping cold-junction compensation, or estimating the cold-junction temperature wrongly, turns that error straight into a measurement error.
Next, the limits of the approximation that the Seebeck coefficient can be treated as constant. This tool uses the linear approximation (constant S), but the real Seebeck coefficient of a thermocouple varies with temperature. The standard thermocouple tables (the reference functions of the IEC/JIS standards) build the non-linearity in as polynomials, and for accuracy across a wide range you must use the table or polynomial. The linear approximation is fine for estimates and for understanding the behaviour, but use the standard reference functions for the final accuracy design of an instrumentation system.
Finally, the misconception that the wiring along the way must all be the same metal, and the opposite carelessness. Because the thermocouple voltage is set by the temperature difference between junctions, an isolated metal (terminal, solder) inserted in an isothermal section makes no difference in theory (the law of intermediate metals). But if there is a temperature difference across the terminal block, an unwanted EMF appears there and becomes an error. In practice you use "compensating wire" of the same material as the thermocouple and keep everything up to the terminal block at the same temperature. And reversing the polarity (the + and - wires) flips the sign and badly skews the reading, so take care.
How to Use
Set hot-junction temperature (typically 0–1200 °C for Type K thermocouples)
Set cold-junction temperature (reference, usually 0–50 °C)
Select thermocouple type via Seebeck coefficient (Type K: ~41 µV/°C, Type J: ~55 µV/°C)
Input amplifier gain (1–1000×) to scale millivolt output to 0–5 V or 0–10 V industrial range
Read temperature difference, raw EMF, cold-junction compensation, and final amplified voltage
Worked Example
Type K thermocouple measuring molten steel at 850 °C with cold junction at 25 °C: ΔT = 825 °C, Seebeck coefficient = 41 µV/°C, raw thermal EMF = 33.8 mV. Cold-junction compensation adds 1.0 mV (25 °C reference), yielding 34.8 mV. With 100× amplifier gain, final output = 3.48 V, within standard 0–10 V PLC input range. Accuracy: ±1.1 °C (±0.4% of span).
Practical Notes
Type K (Chromel-Alumel) dominates industrial furnace monitoring; Type J (Iron-Constantan) preferred for 0–750 °C ranges with better linearity below 400 °C
Cold-junction temperature must be actively measured and compensated—a 1 °C drift at reference junction introduces 41 µV error in Type K signals
Millivolt output requires shielded twisted-pair cabling (Category 5e or grounded copper braid) over >10 m runs to prevent 50/60 Hz noise coupling
Gain setting balances noise immunity (high gain amplifies noise) against measurement resolution; 100× typical for ±50 °C span applications