TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Process: In the first step, the heating takes place under nitrogen atmosphere and/or the heating is carried out at a material temperature of 450-600 degrees C and/or in the second step, the heating is carried out at a material temperatures of 750-850 degrees C. In the first step, the heating takes place in the first reaction space. In the second step, the heating takes place in the second reaction space. The first and/or the second reaction space are laid out in such a manner that transport takes place within the reactor without back mixture. During he heating of the first step and/or in the second step, the treated potassium sulfate-containing sludge is transported in a direction from one end of respective reaction space (beginning) to the other end of the reaction space (end). The potassium sulfate-containing sludge in the first step, is fumigated with oxygen-free gas preferably with nitrogen, preferably with nitrogen in a ratio of 0.2-0.22 Nm3/kg relative to the weight of the treated potassium sulfate containing sludge. The flue gas originated in the first step is removed and is supplied to a thermal post-combustion. The residence time of the respective treated potassium sulfate-containing sludge in the first step is adjusted such that at the end of the treatment of the first step the treated potassium sulfate containing sludge contains largely potassium sulfate and elementary carbon. The potassium sulfate-containing sludge in the second step is fumigated with oxygen containing gas preferably with air, preferably with air in a ratio of 0.05-0.5, preferably 0.1-0.2 Nm3/kg relative to the weight of the treated potassium sulfate-containing sludge, where the aeration takes place with oxygen containing gas in countercurrent manner, and the treated potassium sulfate-containing sludge in the second reaction space is moved in a direction, and is circulated continuously by appropriate facilities, and the stream of the oxygen containing gas flows towards the travelling direction of the treated potassium sulfate-containing sludge. The residence time of the potassium sulfate-containing sludge in the second step, is 1-2 hours, preferably 1.25 to 1.75 hours. The residence time of the treated potassium sulfate-containing sludge in the second step is adjusted in such a way that the carbon content during material discharge amounts to less than 0.01%. The heating in the first and second step takes place in an long dimensioned reaction space, and the treated potassium sulfate-containing sludge in the first and second step is transported inside the respective reaction space towards the longitudinal axis from one end of the reaction space (beginning) to the other end of the reaction space (end), where the treated potassium sulfate-containing sludge is transported from the end of first reaction space into the beginning of the second reaction Space, during the residence time of the treated potassium sulfate-containing sludge in the first Step is adjusted in such a way that at the end the treatment of the first Step, the treated potassium sulfate-containing sludge contains a large extent of pure potassium sulfate and elementary carbon, and the residence time of the respective treated potassium sulfate-containing sludge in the second Step is adjusted in such a manner that it amounts to 1-2 hours, preferably 1.25 to 1.75 hours. The heating in the first Step and/or the second Step takes place in a rotary tube of a rotary kiln designed with storage rings and heated over the outer wall. The rotating tube or the pipe of the rotary Kiln rotates during heating of the first and/or the second step or during the first and/or second Step around the longitudinal axis. The rotating tube or the rotary Kiln at the inner side exhibits devices cantilevered to inner side, preferably over the total tube length, where the devices cantilevered to the inner side are e.g. executed as lifting scoops, preferably devices cantilevered to the inner space, where the device transports the treated potassium sulfate-containing sludge in the direction of the longitudinal axis. The heating in the first step and/or the second step take place in an open-hearth furnace, preferably in an open-hearth furnace equipped with spatula and gas inlet and exhaust vents, which can control the heat supply along the material transport. EXAMPLE - No suitable example given.