The emf of a copper-iron thermocouple with its cold junction at \(0{ }^{\circ} \mathrm{C}\) is given by

\[\varepsilon=-13.403 t+0.0138 t^{2}+0.0001 t^{3} \quad \mu \mathrm{V}\]

where \(t=\) temperature \(\left({ }^{\circ} \mathrm{C}\right)\).
Show that the difference in the Thomson coefficient for the two wires is \[7.535+0.1914 t+0.0006 t^{2} \quad \mu \mathrm{V} /{ }^{\circ} \mathrm{C}\]