Diagram 1 - one turbine, one working substance, one compressor, a refrigerant - an option which I will discuss in this post.
The power of the turbine will be superior to the power of the compressor if the system for redistributing heat returns heat in the evaporator - I will try to prove it by dividing the turbine (1) of two identical turbines and the same two turbines them turn on reverse to become compressors - chart 2
If the valve 7a is closed and valve 7b open will work only turbine 1b. Compressor 2b expands and compresses refrigerant R as at enlargement takes heat from the working substance A after the turbine in a heat exchanger 4b to a temperature equal or less to the boiling point of the working substance A so that it liquefies. The heat that we take from the working substance A is transmitted to the liquid working substance in a heat exchanger 5 where compressor 2b compresses the refrigerant R. As I said above compressor 2b is a reverse turbine 1b so that by conservation of energy should: If power of turbine apply it to the compressor working substance A before the turbine and then the compressor must have the same parameters - temperature, volume and pressure .
Waut b = Win b
The same forces - no change in the parameters of the working substance - no effective unit. There is no way to apply a small force to the compressor so to us remain useful energy because we can not take away heat and give it to another body so that the unit can not hold amounts of heat.
We begin to open valve 7a. Turbine 1a starts. The same one reverse turbine is a compressor 2a, which expands and compresses refrigerant R so that at enlargement in heat exchanger 4a removes heat from the working substance A after turbine 1a to liquefaction. The heat which is removed from the working substance in a heat exchanger 4a return it to the evaporator 3. Pump refers working substance A at a temperature equal or lower than the boiling point of the heat exchanger 4a to the heat exchanger 5.
To compare the forces of tubes 1a and reverse turbine - compressor 2a : Turbine 1a works to a temperature difference T2 / Tbp and produces power Wout. By the laws of thermodynamics - compressor 2a overcomes temperature difference T2 / Tbp so that it would need force Wina equal to the force produced by the turbine Wouta
Wout a = Win a
How does the inclusion of a turbine 1a and compressor 2a of the balance of power Wout b and Winb?? Compressor 2b must give warmth that refrigerant R is accepted at expansion in heat exchanger 4b of working substance A on a large amount of working substance in a heat exchanger 5, because working substance after heat exchanger 4a is collected by the working substance of the heat exchanger 4b. This violates equality Woutb = Winb
Because the compressor 2b to overcome a small temperature difference therefore:
Win b <Wout b
Net power to the entire unit is:
W = Wouta + Woutb - Wina - Winb
Considering that Wout a = Win a
W = Wout b – Win b
So such a unit will have a beneficial force.
As unite heat exchangers 4a and 4b, unite turbine 1a and 1b and compressors 2a and 2b proceed to an efficient engine where Wout > Win - figure 1a
In this line of thinking exchanger 5 may be unnecessary - chart 3 (it is derived from the chart 1 depending on the setting of valves 7)
All waste heat return it to the evaporator 3. This will lead to higher temperatures T2 and a small amount of circulation of the working substance