A temperature difference can generate e. m. f. in some materials. Let S be the e. m. f. produced per unit temperature difference, σ the electrical conductivity and κ the thermal conductivity. Taking M, L, T, I and K as dimensions of mass, length, time, current and temperature, respectively, find the dimensional formula of Z = S²σ/κ.
Options

Question

A temperature difference can generate e. m. f. in some materials. Let S be the e. m. f. produced per unit temperature difference, σ the electrical conductivity and κ the thermal conductivity. Taking M, L, T, I and K as dimensions of mass, length, time, current and temperature, respectively, find the dimensional formula of Z = S²σ/κ.

Options

G1 Physics · Accepted Answer

Thermoelectric coefficient: [S] = voltage/temperature = [ML²T⁻³I⁻¹K⁻¹]. Electrical conductivity: [σ] = [M⁻¹L⁻³T³I²]. Thermal conductivity: [κ] = power/(length × temperature) = [MLT⁻³K⁻¹]. Therefore [S²σ/κ] = [M⁰L⁰T⁰I⁰K⁻¹]. Hence option B is correct.