A head condenser is provided with a plate heat exchanger which has first and second channels through which media can flow and which, for the first medium, form tubes between individual plates that are connected to each other to form a pair of plates and, for the second medium, form waves between pairs of plates that are connected to each other to form a stack of plates. A condenser housing is provided in which the plate heat exchanger is arranged, wherein the condenser housing provides pressure chambers which extend over the large outer surfaces of the plate heat exchanger and are in fluidic connection with the channels for the first or second medium. The pressure chambers are traversed by fluid lines which are in fluidic connection with the respectively other first or second medium.