Research on Boyle's Law and Charles's Law of gas and their applications

    Gases have many different qualities but they commonly have some mutual physical qualities. They are Volume and Density; which are directly affected by Temperature and Pressure and of course in a theoretically, experimentally ideal manner: VOLUME of the Confined Space. Due to this nature, it is not surprising or a coincident when many of our scientists have discovered so many law about gases and they are relatively identical, evidently that all gas's laws have been revolving about the relationship between Volume; Pressure; and Temperature of any experimental gas.
   Some of the gas's laws are: Boyle's Law; Charles's Law; Gay-Lussac's Law; Avogadro's Law; Ideal gas Law etc... In this research article, I'm going to re-mention Boyle's Law and Charles's Law and discussing what are their relationship with the other gas Laws; and finally, what relationship do these gas laws have with our internal combustion engine.

1. What is Boyle's Law?

Boyle's Law is a statement of the relationship between the pressure and volume of gasses. Specifically it states that under conditions of an ideal gas, the product of the pressure and volume remains constant, or
P₁ x V₁ = P₂ x V₂
where P₁ is the pressure before some change, V₁ is the volume before the change, P₂ and V₂ are the new values after the change. Another way of thinking about this law is that the values of pressure and volume are inversely proportional; if one goes up, the other must decrease by the same factor. If you trap gas in a cylinder, and then reduce the internal volume of the cylinder to half its original value, the pressure will double.
   A good example for this is the bicycle hand pump. When you push down on the piston, you feel a resistant force as it may double or triple to compress the volume of the gas 2 or 3 times smaller than initial, and as air is compressed it is pressed into the tyre. Note that the temperature outside and inside the piston are pretty much the same aren't they? 
   So what is the explanation for this? Remember this law only applies on an ideal, theoretical basic. Which means gas in a confined( limited) space is actually moving molecules loosely spaced with each other, and Volume of a fixed amount of gas( fixed amount of molecules) can expand or retract. When the gas expands, the molecules moves faster at a constant speed( ideal gas assumption) and basically their distances get longer. And when they retract because of low temperature, the attracting forces between the molecules get more effective, hence they are closer to each other, but only if the temperature is low enough.
  Now back to the relationship between volume and pressure; at a fixed temperature, change in pressure is inversely proportional to change in volume. That is, because in a confined space, when pressure is applied it presses the molecules closer together; resulting in molecules occupy less space. But during that progress, there is a relatively equal amount of pressure built up due to the molecules being pressed hence bounce against the container and each other, the need for expanding is stored potential. When the pressure is released, the potential energy being pressed now bigger than the pressed threshold, hence the molecules bounce of away each other.


2. Charles's Law:

Charles's law, discovered by Jacques Charles, states that the volume of a quantity of gas, held at constant pressure, varies directly with the Kelvin temperature.  

     Gases expand as they are heated and they contract when they are cooled.  In other words, as the temperature of a sample of gas at constant pressure increases, the volume increases.  As the temperature goes down, the volume decreases as well. Mathematical expression is: V1/T1=V2/T2. This means that the volume is directly proportional to temperature. 
    Explanation: When kept at constant pressure (e.g: 1 atm atmospheric), the temperature can rise high enough to cause the object to expand, gases also. Temperature rises means there is more heat energy participated inside every atom, that all the surrounding electrons orbit faster around the atom. This heat/thermal energy will be released somewhat as kinetic energy as molecules move faster and eventually bounce off away further from each other causing the volumetric expansion. When the temp decrease to a point, the molecules will receive no extra energy and with a constant amount of pressure on them eventually they will stop expanding. This is when attracting force between molecules become effective as mentioned above.


3. Relationship:
   Boyle's law state the relationship between Volume and Pressure @ constant Temperature. Charles's Law state the relationship between Volume and Temperature @ constant Pressure. So through both laws, and their practical proofs, we now know that both Pressure and Temperature have effects on gases's Volume and  Density. Therefore, an expression including Pressure, Temperature and Volume in a relationship is  logically possible. 
   Gay-Lussac's law about gas states that the pressure of a sample of gas at constant volume, is directly proportional to its temperature in Kelvin; and according to that: P1 / T1 = P2 / T2.
So why keep revolving while we can combine all 3 laws into a 3-in-One formula. Because Pressure and Volume are both directly proportional to Temperature, and a change in any of those qualities can result in changes in the other 2 elements so I guess we can make it into the Combined gas law:  

"The ratio between the pressure-volume product and the temperature of a system remains constant".




4. Internal combustion engine:
What are there to be taken into account for an internal combustion? There is the piston; the cylinder provides a confined space, the valves to provide "external breathing"; and the air/ fuel mixture. When the piston moves between TDC and BDC that's the cylinder volume(V1), and when the mixture compressed @ TDC that is the combustion chamber volume(V2). So overall volume of air/ fuel sucked in @ 1st stroke is V1+V2, then it got compressed into V1=> compression ratio inside the engine is "(V1+V2)/V2". 
    
Now what does Boyle's Law explain about the 4 strokes:
Inlet: after exhaust, the cylinder is basically a vacuum as the piston moves down inside the empty cylinder and as the inlet valve open. The pressure difference between atmosphere and the vacuum cylinder sucks the air/fuel mixture filling the whole cylinder=> naturally aspirated, mixture is still under 1atm and original volume and density.
Compression: as soon as the piston reach BDC the inlet valve closes, and the piston starts to move up with (assumed) irresistible pressure. In this stage the appearance of Boyle's law is CLEAR, that when inlet, the pressure is atmospheric, and volume is (V1+V2) but when compressed, the pressure is multiplied and the volume is compressed to only V2, with the same amount of mixture. Note that both Inlet n Compression, the temperature is not allegedly monitored to increase. So we can ideally confirm Boyle's law in this example that  in an internal combustion engine, with the temperature not allegedly varies, the mixture is still the same as when inlet and compression, that the product of initial pressure and volume is still the same after compression. 


Charles's law and internal combustion engine:
The Charles's law reveals itself in the ignition and power stroke of the internal combustion engine. Stating that the volume of the gas expands as temperature increases in a directly proportional manner, it is similar to the air/fuel mixture when it is ignited. From a source of electrical spark at a huge voltage, the electrical energy triggers the thermal chemical reaction, increasingly elevates the temperature of the mixture. Enormous heat energy quickly and continuously passes on to the reacting molecules, pushes them downward powerfully as the whole mixture volume( not chemically the same after combustion) expand rapidly until BDC. So apparently, volume multiplies as temperature elevates. 


5. Some relevant aspect that both Boyle's law and Charles's law haven't covered.
In an internal combustion engine, both petrol and especially diesel, it actually relies on the compression stroke for the mixture to reach combustible temperature. What being said is, compression of gas mixture( air and atomised fuel) actually increases the mixture's temperature. Because as molecules get closer there are collisions and frictions created that leads to the creation of heat, this can be related to kinetic theory and collision theory.