The Seebeck Effect & Thermocouples
Heat a junction, get a current.
Lesson at a glanceShow the key points
- Unequal junction temperatures in a two-metal loop drive a current (thermo-emf).
- Thermoelectric series: cold-junction current from the earlier to the later metal.
- ℰ = aθ + ½bθ² (33.3); θₙ = −a/b; θᵢ − θₙ = θₙ − θ_c (33.2).
- Intermediate metal: ℰ_AB = ℰ_AC − ℰ_BC (33.5); intermediate temperatures: emfs add.
Heat can drive a current directly. Join two different metals in a loop, warm one junction, and charge starts to flow: the Seebeck effect.
The Seebeck effect
Two strips of different metals are joined at both ends to form a loop. If the two junctions are at different temperatures, a current flows. The emf responsible is the Seebeck emf or thermo-emf, and such a pair of metals is a thermocouple. Its size and direction depend on the metals and on the temperatures of the hot and cold junctions.
The thermoelectric series
For junction temperatures between 0 °C and 100 °C, metals can be ranked in a sequence:
antimony, nichrome, iron, zinc, copper, gold, silver, lead, aluminium, mercury, platinum–rhodium, platinum, nickel, constantan, bismuth
- At the cold junction, current flows from the metal earlier in the list to the one later. In a copper–iron couple it flows from iron to copper at the cold junction.
- The farther apart two metals are in the list, the larger the emf.
Neutral and inversion temperatures
Keep a copper–nickel couple’s cold junction at 0 °C and heat the other. The current grows until the hot junction is near 390 °C, then shrinks, vanishes at about 780 °C, and then reverses. With the cold junction at 10 °C the maximum still comes at 390 °C but the reversal moves to 770 °C.
- The neutral temperature θn: where the thermo-emf is greatest. It depends only on the metals (and their purity and treatment).
- The inversion temperature θi: where the emf changes sign. It sits as far above θn as the cold junction sits below it.
Sign convention: ℰAB is positive if the current flows from A to B at the hot junction. With the cold junction at 0 °C and the hot one at θ °C,
The emf is greatest where dℰ/dθ = 0, at θn = −a/b, and returns to zero at θi = −2a/b. If a and b have the same sign there is no neutral or inversion temperature above 0 °C.
A thermocouple’s cold junction is held at 20 °C, and its emf vanishes when the hot junction is at 600 °C. Find the neutral temperature.
Two useful laws
Intermediate metal. With the same junction temperatures throughout, ℰAB = ℰAC − ℰBC. So aAB = aAC − aBC and bAB = bAC − bBC: tabulating every metal against one reference (lead) gives every pair.
| Metal (with lead) | a (µV/°C) | b (µV/°C²) |
|---|---|---|
| Aluminium | −0.47 | 0.003 |
| Bismuth | −43.7 | −0.47 |
| Copper | 2.76 | 0.012 |
| Gold | 2.90 | 0.0093 |
| Iron | 16.6 | −0.030 |
| Nickel | 19.1 | −0.030 |
| Platinum | −1.79 | −0.035 |
| Silver | 2.50 | 0.012 |
| Steel | 10.8 | −0.016 |
Using the table, find a and b for a gold–iron thermocouple, its neutral temperature, and its emf with junctions at 0 °C and 200 °C.
Intermediate temperatures. ℰ between θ₁ and θ₂ equals ℰ between θ₁ and θ₃ plus ℰ between θ₃ and θ₂:
Together these laws mean you can insert extra wires or a galvanometer into a thermocouple circuit without changing its emf, as long as the new junctions are at equal temperatures.
- 1Seebeck: unequal junction temperatures in a two-metal loop give a thermo-emf.
- 2Thermoelectric series: cold-junction current from earlier to later metal; farther apart, bigger emf.
- 3ℰ = aθ + ½bθ² (33.3); θₙ = −a/b, θᵢ = 2θₙ − θ_c (33.2).
- 4Intermediate metal: ℰ_AB = ℰ_AC − ℰ_BC; intermediate temperatures: emfs add.
Check yourself
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