1. Joule's laws of heating
Work done by the electric field on the free electrons in time t is
W = potential difference * charge
= (iR)it = i²Rt
2. If θc, θn, θi are temperature of the cold junction, neutral temperature and inversion temperature respectively
θn – θc = θi - θn
3. Thermo emf depends on temperature with the relation
ЄAB = aABθ + ½ bsub>ABθ²
Where aAB and bAB are constants for a pair of metals A and B.
This gives dЄAB/dθ = aAB + bsub>ABθ
The quantity dЄAB/dθ is called thermoelectric power at temperature θ.
5. Law of intermediate Metal
Suppose ЄAB, ЄAC, ЄBC are emfs from thermocoupes AB,AC, and BC.
If hot junctions and cold junctions of the three thermocouples are at the same temperature,
ЄAB = ЄAC - ЄBC
6. Law of intermediate temperature
Let Є θ1, θ2, represent the thermo-emf of a given thermocouple when the temperatures of junctions are maintained at θ1and θ2. Then
Є θ1, θ2 = Є θ1, θ3 + Є θ3, θ2
7. The actual emf produced in a thermocouple loop is the algebraic sum of the net Peltier effect and the net Thomspon effect.
So emf in a thermocouple loop = ЄAB =
(ΠAB)T - (Π AB ) T0 +(T – T0) (σA - σA)
(More explanation is needed for the formula.)