The below is not an invention, but pure thermo theory. It is based on my insight, that the generally used scientific formulation of the First Law of Thermo is incomplete. In popular terms it says that energy cannot be created from nothing, nor disappear into nothing. In scientific terms it says that the internal energy of a system depends on its condition only (not how it got in that condition).

Naturally, because if we could bring a system from one condition into another, by adding energy to it and then bring it back to the original condition by taking out more energy than added previously, the difference would be energy created from nothing. If less energy is taken out, the difference would have disappeared into nothing.

However, If you change a system's condition fast enough, it may not be in 'balance' yet, after the change of internal energy is completed. There can be temperature gradients within the system, that need time to equalize. During that time, the internal energy doesn't change, but the condition of the system does. Hence, the complete formulation of the First Law should include the term "equilibrium" for the condition of a system. This has great consequences for practical applications, which have been overlooked by all engineers to date (see also this testimonial ).

The application would be using vapors as active medium in a cycle machine. Vapors are media who's condition is close to its saturation condition for a given temperature and pressure range. Wet, or saturated, or not too much superheated water steam belongs to the same category and is thus a vapor too. The choice of medium mainly depends on the desired working temperature range of the cycle.

	Let's consider the typical behavior of any vapor in the PH-diagram (Pressure-Enthalpy Diagram), as shown on the left. Under the dome as shown, such a vapor is in the wet condition, meaning that part of it exists as liquid and part as gas at the same pressure and temperature. Under the dome, the lines for temperature and pressure collapse and remain constant, while the enthalpy of the medium (i.c. its internal energy), as given by point 1, can change between the saturation points 1' and 1" (double quotes denote gas, single ones liquid)(). The left border line of the dome is the saturation line for liquid and the right border line for that of gas.
The area left of the liquid saturation line is for under-cooled liquid, where the temperature lines go straight vertically and the area right of the gaseous saturation line is for super-heated gas, where the temperature lines are slightly curved close to the saturation line, but go rather vertically further away from it. Let's consider the end stages of compression and expansion for a wet vapor, where the compressed condition can be at ambient temperature and thus the expanded condition is below that temperature. This is shown in the next PH-diagram.
	At the compressed start condition, the wet vapor is considered to be fully saturated, thus containing saturated liquid in point 1' and saturated gas in point 1" and its enthalpy being in point 1. When this vapor is expanded to the condition 2 by doing work, while there is no heat-exchange with the environment assumed, its liquid and gaseous components remain in the saturated condition and thus the points 2' and 2" are valid (the detailed course of the expansion process, involving the interaction of liquid and gas, is a rather complicated one and for simplicity I therefore leave it out of consideration here).
During this expansion, work has been done on the shaft and so the internal energy of the medium has decreased with the according change of enthalpy DH. By compressing the vapor again, adding the same change of internal energy DH as compression work, the "incomplete" First Law of Thermo says we must come back in the condition of point 1. However, if we would have a method to separate liquid and gas AFTER completed expansion and compress both to the same pressure, the gaseous part will be compressed adiabatically into super-heat, following the isentrope between points 2" and 1c", while the incompressible liquid part simply increases in pressure, with no change of its (low) temperature and enthalpy - it becomes under-cooled in point 1c'.

Nevertheless, the total enthalpy of the medium is back in point 1, as required by the First Law, but is it in the same 'condition' as before? No, because the original 'condition' was a saturated one (1' and 1") and the re-compressed condition is a combination of super-heated gas and under-cooled liquid.

Immediately after re-compression, we actually have a cold liquid below ambient temperature and a warm (hot) gas above ambient temperature and if we can keep those thermally separated from each other, the cold liquid can absorb heat from ambient (or any external source), while the hot gas gives off the same amount of heat to ambient (or any warmer reservoir) and the condition of the vapor becomes the saturated one in point 1' and 1", while no change of the medium's internal energy occurs during the process (as much went out, as what came in).

The First Law doesn't give any preference for either process and so heat can flow from a colder to a warmer region, with no net resulting work done!

However, this is in the ideal case only. A practical machine has friction and thus more heat must be cooled off than what was absorbed and the difference must be applied as drive power. In practice, there will thus not be a spontaneous process, but yet one that needs very little drive power, much less than what present machines require.

If we cannot (or want not) separate liquid and gas after expansion and instead compress the mixture in full heat exchange between the two parts, we get a totally different behavior, already observed by James Watt at the time, my analyzis of which resulted in the supertrope COMPEX cycle, allowing full conversion of applied heat to mechanical power, as explained here

I hope that some developer will hire me as a consulting engineer, to move thermo science and technology into the 21st century (no claims on intellectual property from my side). If you who read this would be such a possible developer, please contact me.

Rudolph N.J. Draaisma

CONSULTING ENGINEER
Energy conversion and recovery systems
CAD drawings &Techn. calculations.
Techn. descriptions & illustrations
Translations, Documentations
Patent advice and research
website: www.draaisma.net/alternative_engineering/