Seebeck Coefficient Calculator
Enter Seebeck coefficient and temperature difference to compute thermoelectric voltage V=S·ΔT. T-type 41 μV/K, ΔT=100 K → V=4.1 mV; K-type at 1000 K → 41 mV.
Input Data
Results
At a glance:The Seebeck effect (Seebeck 1821): when two different metals or semiconductors form junctions at different temperatures, an EMF — the thermoelectric voltage — appears in the loop. Formula V=S·ΔT, with S the Seebeck coefficient (V/K, a material property) and ΔT the junction temperature difference. A thermocouple of two metals A, B has effective S=S_A−S_B. Common thermocouples: T-type (Cu-Constantan) S≈41 μV/K; K-type (Chromel-Alumel) S≈41 μV/K; J-type (Fe-Constantan) S≈55 μV/K. Semiconductor thermoelectric Bi₂Te₃ S≈200 μV/K, far more efficient than metals. History: Seebeck discovered it in 1821; Peltier found the reverse (current cools) in 1834; Thomson derived the thermoelectric equations in 1851. Applications: (1) temperature measurement — thermocouples span −200 to 1700 °C, an industrial standard; (2) thermoelectric power — RTG (radioisotope heat source + thermoelectric material) powers space probes; (3) waste-heat recovery — industrial exhaust, automotive; (4) Peltier cooling — semiconductor coolers for small fridges and CPU cooling; (5) biosensors — thermocouples measure body temperature.
Formula
Thermoelectric voltage: V = S·ΔT (V)
Thermocouple: V = (S_A − S_B)·ΔT
Peltier coefficient: Π = S·T (W/A)
Thomson coefficient: τ = T·(dS/dT) (V/K)
Thermoelectric efficiency: η = (1−T_c/T_h)·√(1+ZT)/(1+√(1+ZT)+T_c/T_h)
$$V = S\cdot\Delta T, \quad S_{couple} = S_A - S_B, \quad \Pi = S T$$How to Use
- Enter Seebeck coefficient S (V/K) and temperature difference ΔT (K).
- The tool computes V=S·ΔT, output in V, mV and μV.
- Common: T-type 41 μV/K, ΔT=100 K → 4.1 mV; K-type at 1000 K → 41 mV.
Case Studies
Industrial furnace temperature measurement
A K-type thermocouple in a 1000 °C furnace with the cold junction at 25 °C (ΔT=975 K).
V=(S_A−S_B)·ΔT≈41 μV/K×975≈40 mV — read by the instrument and converted to temperature.
Thermocouples cover −200 to 1700 °C and resist high temperature and vibration, an industrial standard.
Space RTG and waste-heat power
An RTG uses Pu-238 decay heat (~1000 K source, ~300 K sink) with Bi₂Te₃ (S≈200 μV/K) to make electricity directly.
Voyager 1 (1977) carries three RTGs totalling ~470 W, still ~220 W in 2024 after 47 years.
Ground waste-heat recovery: automotive exhaust and industrial flue gas drive thermoelectric modules to reclaim energy.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.