The Drop Down Cycle (Part 3 of 3)

In part two of Criminal Clouds, it was explained that hydrostatic lapse and the Second Law of Thermodynamics are incompatible. This may lead some to consider hydrostatic lapse to be a fictitious phenomenon. However, the alternative in which a static body of gas has a uniform temperature throughout, can be shown to be incompatible with the Law of Conservation of Energy.

Let me introduce the Drop Down Cycle, a power cycle that would be able to create energy in the absence of hydrostatic lapse; directly in defiance of the Law of Conservation of Energy.

Operating in an isolated system, under ‘idyllic’ conditions and in the absence of hydrostatic lapse . The Drop Down Cycle consists of two columns of differing heights, containing the same ideal gas. The exchange of gas between these columns, is facilitated at their base by an isentropic compressor. Whist at their tops by a more complicated mechanism, consisting of a vessel that can lowered from the top of the tall column by a hoist, where it connects with an isentropic expander that is located at the top of the short column.

Key Characteristics

Before further elaborating on the Drop Down Cycle’s processes and calculating its net energy production, it is important that certain characteristics of the cycle are highlighted:

Under isothermal conditions, the cycle will produce energy so long as the pressure of the gas within the tall column’s base is higher, specifically:

The temperature of the short column’s gas is an independent variable, while the temperature of the tall column is determined by the isentropic compression of gas exiting the short column, specifically:

The height differential between the two columns must be such, that the pressure ratio of the column’s tops are the same as the column’s bottoms, specifically:

Because the pressure ratio of the tops and the bases of the columns are equal, the isentropic expander will lower the temperature of the gas exiting the tall column (via the vessel) to that of the short column, specifically:

In situations with no hydrostatic lapse, it is appropriate to utilise the isothermal barometric formula to determine the pressure at the tops of the columns, specifically:

Because the pressure ratios must be the same for the tops as they are for the bases, we can substitute in the formulas for the pressure at the tops of the columns and solve for the height of the tall column:

Energy Production of the Cycle

With the requirements of the Drop Down Cycle stated, we can now proceed with calculating the net energy production of the cycle, by calculating the energy input or output of each of the eight steps, specifically:

In the first step, gas is expelled from the base of the short column into the Isentropic Compressor. This is an isobaric expansion process calculated by the below formula:

In the second step, the Isentropic Compressor increases the pressure and temperature of the gas, to that of the tall column at its base. This is an isentropic compression process, which can be calculated with the below formula:

In the third step, gas is expelled from isentropic compressor into the tall column. This is an isobaric compression process calculated by the below formula:

In the fourth step, gas is expelled from top of the tall column into the vessel. This is an isobaric expansion process calculated by the below formula:

In the fifth step, the Vessel is lowered to the top of the short column. In this process, gravitational potential energy is converted into mechanical energy, via the lowering of the Vessel filled with gas, from the top of the tall column to the top of the short column. The energy conversion can be calculated by the following formula:

In the sixth step, gas is expelled from the Vessel into the Isentropic Expander. This step does not produce or consume energy, as it occurs via simultaneous isobaric compression and isobaric expansion, specifically:

In the seventh step, the Isentropic Expander, decreases the pressure and temperature of the gas to that of the short column at its top. This is an isentropic expansion process which can be calculated with the below formula:

In the eighth step, gas is expelled from isentropic expander into the short column. This is an isobaric compression process which can be calculated by the below formula:

The formula for each step can now be substituted into the formula for the net energy production of the Drop Down Cycle:

Conveniently, the two isentropic steps and the four isobaric steps cancel each other out, leaving only step five. This is the step that yields energy from the lowering of the gas filled Vessel, hence the name Drop Down Cycle:

Because the height of the tall column is a dependent variable, its formula can be substituted in, leaving us with a formula containing only independent variables:

Conclusion

While it is clear from the formula, that the Drop Down Cycle would yield energy under isothermal conditions. It is important to recognise, that the cycle does not result in the temperature or pressure of either column changing at its completion. This means the cycle has not transformed energy within the system into the energy yielded, but rather the energy produced has been created. This makes the Drop Down Cycle a perpetual motion machine of the first kind.

The reason that the Drop Down Cycle is able to create energy, in defiance of the Law of Conservation of Energy, is because the isothermal conditions under which it operates are fictitious. Hydrostatic lapse is a consequence of particles trading their thermal energy into gravitational potential energy, as they move from a low position to a high position. If a static body of gas was isothermal, gravitational potential energy would be created each time gas particle moved to higher position. It is this created gravitational potential energy that is converted into mechanical energy, in the Drop Down Cycle.

While Hydrostatic Lapse is a phenomenon that is not consistent with the Second Law of Thermodynamics, its alternative is not consistent with the Law of Conservation of Energy. Ultimately, we have arrived at a situation where these two laws are in conflict. As the Law of Conservation of Energy is effectively the First Law of Thermodynamics, it could be argued that it is a more senior law of physics.

This conflict is a serious issue for physics that urgently needs to be addressed through empirical observation. Please help spread the word about this conflict by sharing Criminal Clouds, so that those with the means to conduct experiments become aware of this conflict. Thank You