Artificial heat sources cause the base of stable air layers which are at ground level in rural regions to become elevated over urban areas. An intervening layer characterized by an adiabatic lapse rate is formed. Within this layer pollutants are trapped and mixed in the vertical. A model is presented for the urban heat island which is based upon the above premises and the first law of thermodynamics. It is a modified version of an advective model first advanced by Summers. The modification consists of the introduction of two heat sinks which permit an extension of the model downwind from the center of the city. (Modified author abstract)