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Thomson Coefficient

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)

Differentiating again both sides with respeet to temperature T we get

d2E = 2c

(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    

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

= 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

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