Incoming and outgoing solar radiation couple with heat exchange at Earth's surface to drive weather patterns that redistribute heat and moisture around the globe, creating an atmospheric heat engine. Here, we investigate the engine's work output using thermodynamic diagrams computed from reanalyzed observations and from a climate model simulation with anthropogenic forcing. We show that the work output is always less than that of an equivalent Carnot cycle and that it is constrained by the power necessary to maintain the hydrological cycle. In the climate simulation, the hydrological cycle increases more rapidly than the equivalent Carnot cycle. We conclude that the intensification of the hydrological cycle in warmer climates might limit the heat engine's ability to generate work.