It is the amount of heat absorbed r evolved in Joules between two points of the same conductor which differ in temperature by 1⁰C when one ampere of current flows for one second. It is denoted by σ.

Characteristics of Thomson Coefficient: (i) It is not constant but varies with the temperature.
(ii)It is numerically equal to the difference of potential per ⁰C.

(iii) It is also known as the specific heat of electricity.

Example. The thermo-electric e.m.f. of a thermo-couple at any temperature 1⁰C is given by E=a+bt+ct2 where a,b and c are constants, Find (a) neutral temperature (b) Peltier coefficient and (c) Thomson coefficient.

Solution: Thermo-electric e.m.f. E= a+bt+ct2 = a+b (T-273) +c(T-273)2

where T is temperature in absolute degrees
Differentiating both sides w.r.t. temperature T we get

dE = b + 2c(T-273)
dT

Differentiating again both sides with respeet to temperature T we get

d²E = 2c
dT²

(a)    Since at neutral tempeture, dE will be equal to zero therefore, substituting T=TN and dE = 0 in expression we get                     dT                                                                               dT

0 = b + 2c(Tn-273)
or (Tn-273) = -b    
                    2c

or          tn = -b  in degrees (centigrade)
                  2c
                                                 
(b)    Peltier coefficient π = absolute tempeture x Rare of change of the total e.m.f.
                                          With respect to temperature = T dE
                                                                                         dT

= T [ b + 2c (T-273)] =T(b + 2ct)

(c)    Thomson coefficient σ  = Absolute tempeture x Rate of change of thermo-electric
                                                Power with respect to tempeture.

 = T d²E = T x 2c = 2cT
      dt²

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