Electrolysis device for the electrolysis of water, having: - at least one electrolysis cell, wherein the electrolysis cell comprises an anode space having an anode and a cathode space having a cathode, wherein the anode space is separated from the cathode space by means of a proton exchange membrane, and the anode space is suitable for receiving water and oxidizing it at the anode to give a first product comprising oxygen and the cathode space is suitable for receiving water and reducing it at the cathode to give a second product comprising hydrogen; - a first gas separating apparatus for the separation of oxygen; wherein the first gas separating apparatus is arranged above the electrolysis cell for the purposes of performing a natural circulation of water, - a first line which is connected to an upper section of the anode space and to the first gas separating apparatus and - a second line which is connected to the first gas separating apparatus and to a lower section of the anode space, - a second gas separating apparatus for the separation of hydrogen; - a third line which is connected to an upper section of the cathode space and to the second gas separating apparatus; - a fourth line which is connected to the second gas separating apparatus and to a lower section of the anode space and/or cathode space, wherein the second gas separating apparatus is arranged above the electrolysis cell for the purposes of performing a natural circulation of water, wherein a first heat exchanger is arranged in the second line and a second heat exchanger is arranged in the fourth line and the first heat exchanger and the second heat exchanger are thermally coupled, and - the second line and the fourth line are connected via a connection line for the purposes of water equalization, wherein the natural circulations of water take place naturally due to the density differences of the water and the products, without the use of pumps. - at least one electrolysis cell, wherein the electrolysis cell comprises an anode space having an anode and a cathode space having a cathode, wherein the anode space is separated from the cathode space by means of a proton exchange membrane, and the anode space is suitable for receiving water and oxidizing it at the anode to give a first product comprising oxygen and the cathode space is suitable for receiving water and reducing it at the cathode to give a second product comprising hydrogen; - a first gas separating apparatus for the separation of oxygen; wherein the first gas separating apparatus is arranged above the electrolysis cell for the purposes of performing a natural circulation of water, - a first line which is connected to an upper section of the anode space and to the first gas separating apparatus and - a second line which is connected to the first gas separating apparatus and to a lower section of the anode space, - a second gas separating apparatus for the separation of hydrogen; - a third line which is connected to an upper section of the cathode space and to the second gas separating apparatus; - a fourth line which is connected to the second gas separating apparatus and to a lower section of the anode space and/or cathode space, wherein the second gas separating apparatus is arranged above the electrolysis cell for the purposes of performing a natural circulation of water, wherein a first heat exchanger is arranged in the second line and a second heat exchanger is arranged in the fourth line and the first heat exchanger and the second heat exchanger are thermally coupled, and - the second line and the fourth line are connected via a connection line for the purposes of water equalization, wherein the natural circulations of water take place naturally due to the density differences of the water and the products, without the use of pumps.