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Equation of Thermo E.M.F. Curve

If the cold junction is at 0oC and the hot junction is at any temperature say ToC, then equation of thermo-e.m.f. can be written as

E = pAB T + 1 qAB T2

where pAB and qAB are characteristic contents of combination of metals A and under conderation and are known as thermo-electric coefficient and E is e.m.f. in micro-volts.

However if cold junction instead of being at 0oC  is at T1oC and the hot junction is at T2oC then the above equation is written as

E = pAB ( T2-T1) + 1 qAB ( T22 -T12 )

As discussed above the e.m.f. is at neutral temperature and e.m.f.

will be maximum when dE is zero.

Differentiating expression T we get

dE   = pAB + qAB T

The temperature T, at which dE will be the neutral temperature.

Hence                0 = pAB + qAB Tn

or                       Tn =  -pAB

The temperature of inversion T , is the temperature at which the e.m.f. is zero and starts reversing. Hence substituting E= 0 in equation we get

0 =  pAB T1 + 1qAB T12

or         T1-2pAB

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