Water extraction device for extracting water from an inlet air stream, - comprising a sorption element for the sorption of water from the inlet air stream and for releasing water to a moisture-laden air stream that is conducted through the water extraction device, wherein the sorption element is arranged in such a way that the inlet air stream and the moisture-laden air stream can flow through it, - comprising a heat supply device for heating the moisture-laden air stream before it flows through the sorption element such that the release of water to the moisture-laden air stream is improved, and - comprising a first condensation stage having a condenser for extracting water from the moisture-laden air stream, characterised in that the water extraction device comprises a compressor for compressing the moisture-laden air stream, which is arranged between the sorption element and the first condensation stage and increases the absolute humidity of the compressed moisture-laden air stream, wherein between an intake side and a pressure side of the compressor the compressor achieves a quotient of final pressure divided by suction pressure, designated as the pressure ratio, of more than 1.3, the water extraction device comprises a second condensation stage having a condenser, wherein the second condensation stage is arranged in such a way that the moisture-laden air stream flows through it in the flow direction after the first condensation stage, and the water extraction device comprises an expansion machine, which is arranged in such a way that the moisture-laden air stream flows through the expansion machine after the second condensation stage. - comprising a sorption element for the sorption of water from the inlet air stream and for releasing water to a moisture-laden air stream that is conducted through the water extraction device, wherein the sorption element is arranged in such a way that the inlet air stream and the moisture-laden air stream can flow through it, - comprising a heat supply device for heating the moisture-laden air stream before it flows through the sorption element such that the release of water to the moisture-laden air stream is improved, and - comprising a first condensation stage having a condenser for extracting water from the moisture-laden air stream, characterised in that the water extraction device comprises a compressor for compressing the moisture-laden air stream, which is arranged between the sorption element and the first condensation stage and increases the absolute humidity of the compressed moisture-laden air stream, wherein between an intake side and a pressure side of the compressor the compressor achieves a quotient of final pressure divided by suction pressure, designated as the pressure ratio, of more than 1.3, the water extraction device comprises a second condensation stage having a condenser, wherein the second condensation stage is arranged in such a way that the moisture-laden air stream flows through it in the flow direction after the first condensation stage, and the water extraction device comprises an expansion machine, which is arranged in such a way that the moisture-laden air stream flows through the expansion machine after the second condensation stage.