A Curious Result: A Combined Heat-Pump and Rankine Cycle Which Supplies Work and Cold Air to the Ambient

Abstract

The Kelvin-Plank statement of the Second Law of Thermodynamics states that work cannot be taken from a constant temperature reservoir without putting energy in first. This means a device cannot be built that produces work from ambient air temperature without a constant supply of work or heat into the device. However, this paper presents the analysis of a particular coupling of two cycles that appears to do just that. The machine combines two thermodynamically matched cycles: a heat-pump cycle and a Rankine cycle. Each cycle runs the other, with the net result being shaft work available to the ambient and an exhaust product of cold air. The only input to the machine is 12°C air from the ambient atmosphere. The heat-pump uses ammonia as the working fluid, absorbing heat from ambient atmosphere and supplying heat to the Rankine engine boiler. The Rankine cycle expansion engine uses propane as the working fluid, and supplies shaft work to power the heat-pump compressor. Using standard, well-known analysis, the net result is a machine that, once started, supplies work and cold air to the ambient with no further work input. Under ideal analysis, the heat-pump operates with a coefficient of performance of 6.85 and the Rankine cycle operates with an efficiency of 21%. Multiplying these gives a combined cycle efficiency of 1.44. The heat-pump superheater operates at an average temperature of −44°C, with a mass flow rate of 1.00 kg/s. It absorbs 106 kW of heat from ambient temperature air and supplies that heat to the Rankine cycle boiler. The Rankine cycle expansion engine has a mass flow rate of 2.51 kg/s, and produces 364 kW of work. Of this, 254 kW is supplied to the heat-pump compressor, 4 kW to the Rankine cycle feed-pump, and the remaining 106 kW of work to the ambient. This equals the heat extracted from the ambient; there is no unexplained creation of energy. All analysis was performed from standard engineering text books, and all thermodynamic data was taken from common industry charts. The cycles are common and well known, and the temperatures, pressures, and expansion ratios well within believable values. The analysis has been peer reviewed and no errors found. Yet when these two cycles with these two working fluids are combined, the result is net work to the environment and cold air, with no work or heat input. The authors do not believe the second law is flawed. We expect an error will be discovered, either in our analysis or in the thermodynamic tables of the two fluids that we used. We present the analysis and result in the hopes of having the error pointed out.