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Battery and energy materials

A thermoelectric material at 300 K has a Seebeck coefficient of 200 µV/K, an electrical conductivity of 1.0×10⁵ S/m and a thermal conductivity of 1.5 W/(m·K). Which value is closest to the dimensionless figure of merit ZT = S²σT/κ?

  1. AAbout 0.0027
  2. BAbout 0.8
  3. CAbout 4000
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Answer: B. About 0.8

The power factor is S²σ = (200×10⁻⁶)² × 1.0×10⁵ = 4.0×10⁻⁸ × 1.0×10⁵ = 4.0×10⁻³ W/(m·K²). Multiplying by the temperature and dividing by the thermal conductivity gives ZT = 4.0×10⁻³ × 300 / 1.5 = 0.8. About 0.0027 forgets to multiply by the temperature T; ZT becomes dimensionless only once temperature is included. About 4000 forgets to square the Seebeck coefficient. Bi₂Te₃-based materials used near room temperature have a ZT of about 1, and the larger ZT, the closer the heat-to-electricity conversion efficiency approaches the Carnot efficiency set by the hot- and cold-side temperatures.

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