Consider the following theoretical cycle. There should be a flaw somewhere, but I could not find it yet and will appreciate it if someone can point it out to me. A lot of ideal assumptions are made, such as reversible heat transfer, but it is not intended to be practical, as long as it adheres to allowable theoretical ideal assumptions. Two identical expandable vessels regulated to be at independent constant pressures using some means, i.e. connected to an external constant pressure source, contain equal amounts of a saturated fluid. These vessels are insulated in the sense that no heat is lost to the surroundings, however, heat can be transferred between them and provided by an external source, therefore they are not strictly adiabatic. Both vessels are placed in a liquid body of significant depth. The liquid is assumed to have no appreciable change of density with pressure (height). Step 1: One vessel starts of with all fluid in a saturated liquid form (vapour fraction 0). The combined density of the vessel and fluid in liquid form allows it to sink to the bottom of the liquid body. The second vessel starts with all fluid in the saturated vapour form (vapour fraction 1). Since both vessels are at equal pressure, the second vessel is expanded significantly without an increase in its mass, causing its overall density to be very much less than the density of the body of liquid it is immersed in, and it floats on top. A thermally conductive link is made between the two vessels, allowing thermal energy to be transfered between the two vessels. In order for heat transfer to occur, a thermal gradient will be needed. This can be accomplished by dropping the regulated pressure of the vessel at the bottom of the body of liquid by an infinitesimal small amount, causing some vapour to flash and the temperature of the fluid to drop infinitesimally. (To the same degree that the gradient it infinitesimal, the heat transfer will take an infinite amount of time to complete, but I do not believe that is a crippling condition, I will return to this later.) Thermal energy is now transferred from the fluid at the top of the liquid body to the fluid at the bottom of the liquid body until the fluid in the first vessel is saturated liquid and the fluid in the second vessel is satrurated vapour. Step 2: The vessel originally at the top of the body of liquid now has an overall density that is greater than the density of the liquid, and it sinks to the bottom. Connecting that vessel to a pulley system allows it to do work on the pulley consisting of the net downward force times the distance. If the vessel is dropped infinitesimally slowly, the drag force can be eliminated for simplicity, but this is not a necessary condition. Likewise, the vessel now filled with vapour at the bottom of the liquid column rises to the surface and can do work on a pulley system. Step 3: The vessel now at the top of the liquid body needs to be restored to the initial condition for the vessel at the top of the body of water mentioned in Step 1. This is done by increasing the pressure regulated pressure to its initial amount before it was dropped in Step 1 to allow for heat exchange to take place. Some of the fluid will condense and latent heat needs to be supplied until all of the fluid is in the vapour state again. The amount of heat required will be infinitesimal for an infinitesimal pressure drop, and will be larger for a larger pressure drop in Step 1. Now, as long as the heat required to restore the system to its original state is less than the work done on the pulleys in Step 2, this cycle is outputting net work, which can't be right. Since these two steps are not directly related in any way, there appears to be no obvious reason why they should cancel out, and they do not appear to do so if all processes are taken to occur infinitely slow, maintaining reversibility. I will appreciate comments. Please let me know if something is unclear. If a more quantitative argument is preferred, I will supply it as soon as possible, but I expect that most people acquianted with thermodynamics will get the basic idea. Thank you in advance.