Thomson Heat Evolution
Thomson’s effect was discovered by Thomson (later called Kelvin). According to this effect, if two parts of a single conductor are maintained at different temperatures, an e.m.f. is developed between them. The e.m.f. so produced is called Thomson’s e.m.f. If the steady current is passed through an unequally heated conductor, an absorption or evolution of heat in excess of Joule’s heat, takes place in the conductor.
Thus Thomson’s effect is the absorption or evolution of heat in excess of Joule heat when current is passed through an unequally heated conductor. Thomson effect is reversible effect.
To understand Thomson’s effect, consider an unequally heated rod AB of copper. Let the end A of the be at higher temperature than its end B. on passing the current from A to B in the rod, heat is evolved along the length of the rod. In case, the current is passed in the rod from end B to A, the heat is absorbed along the length of the rod. It is accounted due to the fact that in case of copper, the hot end of the rod is at higher potential and its cold end is at lower potential. When current flows from hot end to cold end of copper rod i.e. from higher potential to lower potential, the energy is produced which is radiated out in the form of heat. When current is flowing from cold end to hot end of the copper rod i.e. from lower potential to higher potential, the energy required which accounts for the absorption of heat energy. Thomson’s effect for copper is positive. Other substances showing positive Thomson’s effect are Sb, Ag, Zn etc.
There are some other substances like Fe, Co, Bi, Pt etc. for which Thomson’s effect is negative. It means for such metals, Thomson’s effect is just reverse as that for copper. It means, according to Thomson’s effect for iron rod, heat is absorbed when current is passed from hot end to cold end and heat is evolved when current is passed from cold end to hot end of the rod.
For lead, Thomson’s effect is nil. It means no heat is evolved or absorbed when current is passed through an unequally heated rod of lead. It is due this reason that lead is used as a reference metal in thermoelectricity.
Thomson’s coefficient: Thomson’s coefficient is defined as the e.m.f. that exists between the two points of a uniform conductor which has a temperature difference of 1°C (or 1K). it is denoted by σ.
Let dV = potential difference between two points of a metal rod.
dT = temperature difference between the same two points of rod.
Then Thomson’s co-efficient of the rod is given by
σ = dV/dT or dV = σ dT
total Thomson’s e.m.f. between temperature T1 and T2 of a metal rod is given by
V = ∫T1T2σ dT
Thomson’s co-efficient is also defined as the amount of heat energy evolved or absorbed between the two points of a conductor maintained at a unit temperature difference when unit current is passed for one second through the conductor.
If current I flows through a conductor for time t, then the amount of heat energy evolved or absorbed between the two points of the conductor maintained at a unit temperature difference is given by
Q = σ It.
If S, ∏ and σ are the Seebeck, Peltier and Thomson’s coefficients, then it can be established that ∏ = T(dE/dT) = TS
σ = - T(d2E/dT2) = - T(d/dT) (dE/dT) = - T(dS/dT)
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