A temperature difference can generate e.m.f. in some materials. Let S be the e.m.f. produced per unit temperature difference between the ends of a wire, σ the electrical conductivity and κ the thermal

Question

A temperature difference can generate e.m.f. in some materials. Let S be the e.m.f. produced per unit temperature difference between the ends of a wire, σ the electrical conductivity and κ the thermal conductivity of the material of the wire. Taking M , L , T , I and K as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity Z = κ S 2 σ ​ is :-

TestHub · Accepted Answer

​ S = emf per unit temperature difference σ = Electrical conductivity k = Thermal conductivity [ S ] = [ ML 2 T − 3 I − 1 K − 1 ] [ σ ] = [ M − 1 L − 3 T 3 I 2 ] [ K ] = [ M 1 L 1 T − 3 K − 1 ] [ Z ] = K S 2 σ ​ = [ M 1 L 1 T − 3 K − 1 ] [ M 1 L 1 T − 3 K − 2 ] ​ ​ [ Z ] = [ K − 1 ]

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