A device for evaporating a predeterminable volume of fluid provides for successive addition of partial volumes of the predeterminable volume to a supply line at different adding rates, at least partially evaporating the partial volumes forming a vapor film between them and a supply line wall, conveying the partial volumes through the supply line to an evaporator surface, and applying the partial volumes to an evaporator surface region varying as a function of mass and/or volume adding rate of the partial volume, permitting effective evaporation of fluid, particularly urea/water solution. Utilization of the highest possible proportion of evaporator surfaces is achieved by mass and/or volume addition rate-dependent distribution of impingement surfaces on the evaporator surface. This heating strategy in the supply line region ensures the Leidenfrost effect when individual partial volumes are added. As even a distribution as possible is achieved using a corresponding geometrical configuration of the evaporator channel.