Combustion engine and Carnot formula

We are analyzng here only four-stroke diesel engine, but the conclusions are generally valid for any other internal combustion engine .
A mixture of air and vapor of the liquid fuel explodes when it comes into contact with a flame or by self-ignition and the heat generated in the expansion phase of the gases can be used for mechanical work. Based on this principle, with small variations, different types of combustion engines can be designed.
Schematically, a diesel engine has one or more cylinders fitted with pistons whose tail is hinged to generate circular motion. The cylinder includes a fuel inlet and two valves, one for air inlet and the second outlet ports from the combustion gases. The two valves are driven by a moving device that synchronize their motion to specific set time intervals.
The principle of operation is as follows:

Figure 6, Time I: Absorption  Assume the piston is at upper end of the the cylinder. The intake valve for air get open and and exhaust valve for gases remains closed. As the piston is drawn into the cylinder, air from the atmosphere is uptaken into cylinder.	Time II: Compression. Intake valve for air closes and the piston compresses the air in the cylinder up to 25-30 at. This compression raises the temperature up to 700-900 ° C.
Fig. 8 Time III : pre Ignition . The piston has reached the upper end of the cylinder.	At this time (Fig. 8 ) , the fuel is injected in the form of fine droplets, the mixture self-ignite, the gases expand and push the piston down (Fig. 9).
Time IV: Evacuation  The piston has reached the lower end of the cylinder. Exhaust valve opens and the piston, under inertia of the movement gained, returns and exhausts combustion gases through it. Figura 10

  Theoretical modeling of heat engines and in fact the apparition of thermodynamics as a branch of physics has experienced a breakthrough after publication by Sadi Carnot of his study entitled 'Reflexions sur la puissance du feu driving propres et sur les machines à developper cette puissance" (in 1824).

It is accepted that in a monothermal cyclic process, only mechanical work can be converted into heat, but not vice versa. In order to obtain the conversion of heat into mechanical work it is necessary that heat machine operates with two heat sources at different temperatures .
Carnot envisioned the working principle for an ideal bithermal reversible machines whose performances has shown to upper limit the yield for any real thermal machines which operate between the same temperature extremes as the Carnot cycle .
Real thermal machines differs from the ideal one because they have moving parts with friction and heat loss and these facts change the energy balance.

Figure 11

In fig. 11 is presented the ideal cycle of a thermal machine often called as ,,the Carnot cycle”. This cycle consists of four processes. Between states A and B there is an isothermal expansion of gas, the cylinder being in thermal contact with the hot source at temperature T1. During this isothermal expansion, the gas receives a quantity of heat Q1 from the hot source.
Then, the contact with hot source is broken and gas undergoes an adiabatic expansion between states B and C. In state C, the gas temperature reaches temperature T2 equal with the temperature of cold source.
In the course of the A - B and B - C transformations, gas molecules produces mechanical work on piston ( pushes it ) and this make the flywheel rotate.
Once reaching the temperature T2, the gas is placed in thermal contact with the second tank heat named cold source. Because of inertia, the flywheel rotates further, while piston is engaged and compress isothermally (at T2) gas between C and D. During this isothermal compression, gas transfers to the heat source an amount of heat Q2. In state 4, the thermal contact with the cold source is interrupted and adiabatic piston compresses the gas to the initial state when the temperature returns to T1.
When the cycle is performed in clockwise direction, this is called direct Carnot cycle. The total work supplied (L > 0), in terms of coordinates p-V in Figure 11, will be the area contained within the cycle, positive by convention.
As you can see, the aria is described by two isothermal curves on sections AB and CD and two adiabatic curves in portions BC and DA. These transformations are considered in ideal conditions and so a engine runnig after this heat cycle would ideally yield :
η = (T1 – T2) / T1
T1 – temperature of warm source
T2 - temperature of cold source
To achieve this performances in practice, the transition from T1 to T2 should be done abruptly, so that vapors do not meet on the road intermediate temperatures and conversions have to be perfectly reversible.
In reality, this efficiency is never attainted and sometimes the yield is quite far from it. As a general idea of heat engine efficiency varies quite broad, as follows:
• Simple steam = 2 %
• Steam refined = 20 %
• Steam turbines = 25 %
• carburettor = 35 %
• Diesel engine = 45 %

Second Principle of Thermodynamics Carnot states the following: All heat engines operating between the same temperature limits have the same maximum output.
Consequences of principle II:
1. You can not drive a integral transformation of heat into mechanical work ;
2. Thermal efficiency of an engine is greater as the temperature difference between the hot source and cold source is higher.
Second Principle of Thermodynamics tells us that for a heat machine to operate needs two heat sources. Therefore, in all heat engines there is a heat reservoir at high temperature, which gives it to a conversion body. It retains and converts some of it and send the rest out at lower temperature .
Actual thermal machines are studied on the basis of the theoretical model offered by Carnot cycle.
For a thermal machine, the transformation of heat into work within the engine cylinder is made by relaxation between a certain value for the pressure, volume and temperature of gases generated in the combustion process and the external pressure and temperature of exhaust gases.

Why the current explanation is completely wrong ....

Experimental part 
For this experiment you can use some old diesel engines, since their functionality is affected affected after experiments.
It is already known that the original diesel engine was designed to use coal dust as fuel; but because the piston and cylinder high corrosion, the engine was further adapted to liquid fuels. Experiments below involve the use of highly reactive substances, therefore experiments must be performed taking necessary precautions.
Once you have got such used engine, the injection galery is blocked and in this way you have the possibility to feed the engine manually and follow the comportment of engine cycle after cycle.
A first fuel to for this engine is represented by magnesium or aluminum as powder.
These metals react with oxygen to form oxides (actually may be formed as a byproduct and nitrides respective secondary reaction due to metal with nitrogen in the air ) by the following reactions:

Both reactions are highly exothermic. Enthalpy of formation of magnesium oxide ΔH = -601 kJ / mol and the oxide of alumniu is ΔH = -1675.7 kJ / mol
We proposed these unusual motor fuels as these oxidation reactions occur with volume contraction. As result of reaction between metal powder and oxygen gas are generated metal oxides which are solid (powder).

The purpose of this experiment is to see what is happen when the fuel generate a strong thermal effect (temperature gradient) but there is a small pressure gradient or in other cases the combustion takes place with a negative pressure gradient.  
Of course, except for small changes the sequences in the cycle are quite the same for the classical fuelled engine.

The principle of operation is as follows:

Time I feeding. The solid fuel is introduced into the cylinder and injection galery is blocked as shown in Figure 17 .

Time II: Absorption. The air inlet valve opens and as piston is drawn into the cylinder, air is sucked from the atmosphere as shown in Fig . 18 .

III: Compression. Air admission valve closes and the piston compresses the air in cylinder up to 25-30 atm. This compression raises the temperature up to 700-900 °C and ussualy  Mg and Al autoignite in this stage.

Time IV : Auto- ignition 

When the piston reaches the upper end of the cylinder the mixture ignite itself. Two different physical phenomena take place: there is a small increase in pressure gradient due to the gas expansion powered by released heat of cumbustion; there is also a decrease of number of gas particles in the cylinder, because oxygen combines with metal and a solid is formed.  
As far these phenomena are opposite, the piston moves from the upper end position but it does not get enough momentum to arrive at the lower point and to perform the entire cycle.
How can we get a mechanical power from an engine wich is not able to give back at least the energy consumed for admission and compression .....?!

Figura 20

I hope to have the chance to repeat the experiments into a more organised research conditions. It will be interested to find the value of pressure generated by such unconventional fuels into cylinder, the effective yield, etc. At a first glance, the efficiency of a motor depends on the relative variation of pressure inside cylinder. Of course this pressure gradient is affected either by a temperature gradient, either by a volume gradient.
Although some experiment are still in progress, and motor behavior requires more detailed studies, some conclusions can already be drawn and these conclusions are not so pleasant for current theoreticians.
Pressure gradient is the driving force of the engine and this gradient is secondary influenced by a change in volume or by a change in temperature.

In practice an engine can work fine with a fuel having a very low combustion heat but able to generate a lot of gases during combustion.
The fact that common fuels are generating both an increased volume  and an increased temperature during cumbustion, due to the exoterm reaction used to power the engine, is only a ,,coincidence" and not the only posibility available.
For scientific purpose, a endothermic reaction generating an volume gradient can also be used to show that in this conditions an engine can produce a mechanical power.
All these considerations require reviewing the entire thermodynamic and certainly, this is not so pleasent ...
A second conclusion concerns the clear distinction between the heat generated during a chemical reaction and how this can be converted into useful work .
So-called ,,heat engines" which we use daily, does not really work on the heat converted into mechanical work but on the difference in pressure generated in the cylinder as a result of a chemical reaction. This gradient of pressure is mainly generated by an increase of volume coming from rection products and secondary by a gradient of temperature due to exotherm character reaction. 
The whole approach to burning and recovering the maximum amount of useful work to be rethought from the ground.
It is necessary for engine designers to consider the recovery of reaction heat and transform it into useful work after the recovering of   useful work generated by the pressure gradient.

To be corrected 
This approach would allow a further reduction in fuel consumption of an engine ( with a percentage of 30 to 50%). Even the heat of condensation of the resulting water in the reaction may be used .
To be more specific consider the combustion reaction of octane :

for this the enthalpy of reaction is ΔH = -5460 kJ / mol .
One mole of octane occupy a volume of about 0.2 L while a mole of gas ( oxygen , water or carbon dioxide ) occupies a volume of 22.4 L. The stoichiometry of the equation shows have that 12.5 moles of oxygen that means 280 liters are consumed during combustion. After burning, all the reaction products are in gaseous form, and such products will occupy 381 L.
At this stage, the combustion heat of reaction is very important and it can not be entirely taken out from the system as it would result in condensation of the gaseous water in liquid form. If we take out the heat of reaction at this stage, we have a volume reduction after burning (only 8 volumes of CO2 on the right) and basically we recover heat but the engine lose the ability to perform work due to changes in volume.
Smart solution would be to recover useful work generated by the chang of volume and then add to the whole process a secondary heat recovery cycle. Of course, this recovered heat can be transformed into mechanical work and is likely to lead to even double the current yield.
Schematically this can be represented as follows:


The resulting combustion pressure gradient ( Differentialpressure ) due to changes in volume and enthalpy of reaction ( ΔH ) due to the formation of new compounds more stable thermodynamically .
The current engine designers converted into mechanical work only L1 Differentialpressure pressure gradient generated during combustion , whilst ΔH is transferred to the environment. But if ΔH is used in a secondary cycle to create a new pressure gradient Ap , it could be converted into mechanical work L2 . In this type of fuel could be recovered (theoretically ) produce and transfer everything back macro system carbon dioxide gas and liquid water .
In order to recover and use the heat of reaction , it is necessary to take into account the thermal insulation of the entire circuit of the engine and the exhaust system . Of course there are many variations of transformation heat of reaction in a secondary pressure gradient . Steam engine using other lower boiling solvent water would be a viable solution . The subject will be resumed and detailed in the book.