An exhaust air dryer includes a process airflow entering from outside as supply air, which removes moisture from laundry introduced in a treatment compartment and which emerges to the outside as exhaust air through an air outlet, a heat exchanger between the treatment compartment and the air outlet, seen in the airflow direction, which removes heat from the process airflow, while forming condensate, a dispersal device arranged downstream of the treatment compartment in the airflow direction and in front of the air outlet, which adds at least part of the formed condensate to the exhaust air, and a hydrophilic body belonging to the dispersal device, which projects into the process airflow and is impinged upon by condensate.
