A device for evaporating a urea-water solution includes a delivery duct for the urea-water solution. The delivery duct extends through at least a first zone and a second zone for the introduction of heat energy. The zones can be heated separately from one another and, in the second zone, the delivery duct initially has a meandering course in a second inlet region, and thereafter has a rectilinear course. A method for evaporating a urea-water solution includes pre-heating the urea-water solution in the first zone to a temperature in a range from 100° C. to 150° C. and evaporating the urea-water solution in the second zone at a temperature in a range from 420° C. to 490° C. In particular, this significantly reduces the tendency for such an exhaust-gas-external evaporator for a urea-water solution to become blocked. A motor vehicle is also provided.