1. For the liquefaction of a given quantity of gas by performing work on it, the amount of heat which will have received liquid substance is equal to the amount of heat the on gas plus heat equivalent of the work done on it
2.The amount of heat which can be converted into mechanical energy of a liquid substance having a temperature higher than its boiling point is equivalent to a difference in temperature to its boiling point
3. The converter of heat into mechanical energy on the last cycle of the working substance in the "external combustion - internal cooling by more than one working substance" converted at less than 50% of the amount of heat
Then we will need to transfer waste heat from last cycle to previous cycles, to enable the latter substance to cool the foregoing, and so the unit to work - diagram 1
Оn this diagram I chose option whereby heat of the last cycle is attributed to the liquefied gases the last working substance and on the evaporator of the previous working substance, but it can distribute heat to all evaporators of the unit.
Comparing the amount of heat and temperature differences of useful and opposite force - the unit would be effective.
Because of the heat that will bring in the evaporators on preceding substances will allow to reduce the flow of pumps -the amount of circulation of the relevant working substance.
In method of heat exchange between liquid and gaseous working substance is not necessarily the last evaporator (n on diagram 2) to be at low temperature. We can have an effective unit in which gases from all evaporators enters the cooler, which returns heat in the evaporator n . His temperature will not be the lowest in the unit, but the useful forces are bigger than the opposite and this option.