We have examined both theoretically and experimentally the thermopower of an asymmetric thermocell, Ag/alpha-AgI/Ag2S, which involves a mixed conductor (Ag2S) as a possible electrode for the system of an electrolyte with common ions (AgI). It has been found that the mixed conductor probe allows one to measure the thermopower of the electrolyte under the Soret equilibrium condition which would be impossible to realize in a symmetric thermocell, Ag/alpha-AgI/Ag. Upon comparison of the stationary state thermopowers from the symmetric and asymmetric cells, the transported entropy of Ag in AgI turns out to be equal to the standard entropy of metallic Ag.