From a thermodynamics perspective, achieving 100% efficiency in a heat engine violates the second law of thermodynamics. This law essentially states that energy systems have inherent inefficiencies and that heat cannot be converted into work with 100% efficiency.

A heat engine operates between two thermal reservoirs at different temperatures (T_hot and T_cold). The maximum possible efficiency of such an engine is given by the Carnot cycle, which is an idealized thermodynamic cycle representing the maximum possible efficiency. The Carnot efficiency is given by:

Efficiency = 1 - (T_cold / T_hot)

where temperatures are measured on an absolute scale like Kelvin.

Some energy is always lost in any real process, often as waste heat. This is due to a property of the universe called entropy, which is a measure of disorder. The second law of thermodynamics can be expressed in terms of entropy by saying that the total entropy of a closed system will always increase over time.

The concept of a double gas thermodynamic cycle is interesting. No cycle, even if it's a double gas cycle or any other type, has been proven to achieve 100% efficiency. Any claim that a heat engine has 100% (or more) efficiency should be critically examined for errors, as it contradicts established physical principles.

While improvements can often be made to increase the efficiency of heat engines (such as by using better materials, reducing friction, or improving the design), the second law of thermodynamics fundamentally limits the maximum efficiency that can be achieved. Even under ideal conditions, some heat energy will always be lost and not converted into useful work.