Estimate the temperature profile of a wire of length L and radius r when an electric current I is driven through it, from the left end to the right end, causing it to heat up. The wire has an electric conductivity σ and a Thomson coefficient τ . The heat is entirely carried by the wire to its ends. The heat dissipated at the surface of the wire and the Joule heating are assumed negligible. The left end is kept at a constant temperature T₀. Determine the temperature profile T (x) along the wire when it has reached a stationary state. Also give an expression for the temperature at the right end in terms of the Thomson coefficient τ and the electric resistance R of the wire.