SB, air conditioning and pressurization in an airliner are tied together for the simple reason that the bleed air coming from the engine is far too hot to be used to pressurize the cabin without first being treated, or conditioned.
Before bleed air can be admitted to the aircraft pneumatic system at all, it must be precooled to a value that won't cause system damage. Typically this is around 350 degrees F. The exact values vary, and aren't particularly important. It's worth knowing that the raw bleed air can be well over six hundred degrees F...which is hot enough to do structural damage as well as harm or kill occupants of the aircraft...so it's pretreated and cooled with a "precooler" which acts as a heat exchanger, or air radiator, before the bleed air is sent to the aircraft pneumatic system.
Once in the aircraft pneumatic system, pressurized air is used for a number of functions which you already identified...these include pressurizing the airplane, heating the interior, actuating things such as leading edge flaps or devices, pressurizing hydraulic resorvoirs and potable water, anti-ice and de-ice, fuel heat, etc.
Pressurization works simply enough; pressurized air is allowed into the "pressure vessle" (the part of the aircraft that's to be pressurized) until a desired value is reached, then the remaining pressure is vented out of the airplane through "outflow valves." The outflow valves open and close as required, usually automatically, to keep the cabin differential pressure constant, or as established by the pilots or flight engineer. The outflow valves also have automatic protective features attached to them through the pressurization system, such as limiting the rate of cabin climb or descent, and altitude limiting (running fully closed to prevent cabin air loss when cabin altitude reaches a particular value---when it climbs too high).
In order to make the pressurized bleed air acceptable for use in the cabin, it has to be conditioned, and this is done through air conditioning packs. Packs usually involve air cycle machines which use expansion turbines and heat exchangers to extract heat energy from the bleed air. The amount of heat energy extracted is is determined by how much airflow is allowed to go through the air cycle machine turbines, and how much is allowed to go around them. Additionally, the use of more than one extraction turbine gives a more precise means of controlling this temperature.
The output from the packs comes in a fairly narrow range. The packs cool the air, and if the temperature is to be increased, then "trim air" from the hot side of the pack is used. Trim air is air that hasn't been through the conditioning process yet; it's hot air that can be mixed with the cooled air to precisely set the desired temperature.
According to information about B787 it won't use engine bleed air (due to the danger of oil wapors in the airstream) but rather AC electric powered pneumatic motor that will deliver pressure to the cabin. Someone also sais that this will incrise overall fuel efficiency.
Any time that bleed air is taken from a turbine engine during operation (save for special bleeds designed for engine operation), the engine's fuel efficiency suffers. If the engine is working hard to move a certain amount of air through the engine and one is taking air away from the engine, then the engine must work harder, or the engine is less efficient. The use of bleed air for anti-ice reduces engine efficiency. The engine runs hotter and may produce less power (thrust). Using electric compressors in lieu of air cycle machines may or may not have benefit, given that the method and size and application are important factors in the equation. You appear to have made up your own mind on that, however, so further discussion is probably unwarranted.
...but this reading has no sense for me. I can say that this configuration will be applied on plane that doesn't use engine bleed air. Planes that do, don't have secondary compressor and heat exchange between as it takes pressure air from the engine itself via light air colectors and pipes. And because we have to maintain fuel temp above -37°C (normal operation altitude OAT is -56), and we also have to maintain wings and engines leading edges above water freezing point (I say 0° C), we have a huge heat consumer - so I don't see the point of any extra heat exchanger.
Why can you say that this configuration (air cycle machine) will be "applied on a plane that doesn't use engine bleed air?"
You state that airplanes using bleed air don't have secondary compressors and heat exchangers...but they do. Multiple heat exchangers, in some cases..and not all of them involve expansion turbines.
What is a "light air collector?"
You appear to further be saying that because you have a need to elevate fuel temperature, you have no need for a heat exchanger.
Fuel temperature is another topic entirely, and numerous methods of affecting fuel temperature are in use. To suggest that it should be the sole means of cooling the cabin air is a bit of a stretch, particularly when considering aircraft that operate in the desert. Further, the outside air temperature isn't necessarily relevant, depending on the fuel system in use, and depending on the fuel tank, and tank location and dimensions in use, too. Additionally, fuel freezing points vary with the type of fuel in use; your temperatures aren't accurate save for a limited range of fuels.
Why do you feel you have to maintain wings and engine leading edges above the freezing point of water? Engine, nacelle, and wing anti-ice is applicable at some times and not at others, and can be quite damaging if used all the time in some applications...to say nothing of the reduction in engine efficiency. Sometimes it's needed and warranted, sometimes it's not. Additionally, compressibility affects the local temperature differently to affect ice formation, and must be considered.
The other thing is that I don't beliewe that you can extract mechanical power from hot air. Car's supercharger (turbine and compresor stage on the same shaft) doesn't use temperature but pressure - meaning it doesn't lower EGT but it only ads backpressure.
Energy is traded between one form and another all the time. Chemical energy for heat energy for mechanical energy and so on. It's how powerplants operate, how we work our engines, how we do nearly everything in the aircraft and in flight. We trade one form of energy for another. We trade burning fuel and spinning turbines for thrust, we use compressed air to pressurize, to move devices, to do all sorts of things. Most certainly you can extract mechanical energy from hot air.
Your understanding of a supercharger is somewhat lacking. You may be thinking or a turbocharger, rather than a supercharger (turbocharger is driven by exhaust gasses, while a supercharger is driven by the engine). You also express a lack of understanding regarding exhaust gas temperatures and both piston and turbine theory.
When you state a "supercharger" adds backpressure, you're talking about a unit in the exhaust stream, which is of course, a turbocharger. A turbocharger extracts energy from the exhaust stream, and uses this energy to turn a turbine wheel. This turbine wheel is mechanically linked, often by a direct shaft, to a compressor wheel in the induction side of the engine. This is entirely unrelated and irrelevant to the function of an air cycle machine, because among other things, the induction air in the ACM isn't being heated by combustion, with more energy being added between induction and exhuast.
You're confusing systems and trying to apply principles from one to the other...but you misunderstand both systems and consequently it's not making so much sense to you.
As far as EGT...yes, it can be affected by both backpressure and by scavenging (tuned exhaust), but it's entirely irrelevant to the function of an ACM, and EGT is a function of combustion, which is directly affected by induction pressure...again, no bearing on a discussion of the ACM. You're clouding the issue by trying to make an example out of an unrelated topic.
You appear to be upset, or displeased with what you've read about the Boeing 787 product. You have that right. However, you appear to be asking a question on the one hand, and on the other attempting to make a point or rally agaisnt Boeing. Which is it? Are you looking to gain an understanding of aircraft pressurization systems, or are you looking to complain about Boeing?
I imagine either one is probably just fine, but you should probably be clear as to what it is that you're trying to accomplish.
I personaly think that there is higher energy heat demand to maintain cabin temperature between 20-24°C than oxygen demand - changing the CO2 rich air. Meaning that it will be waste of air pressure - equal energy if you will maintain tempreature thus constantly applying new warm air.
I have absolutely no idea what you're trying to accomplish with this paragraph. Are you asking a question or trying to explain a new theory? Changing CO2 rich air? What CO2 rich air?
What is a waste of air presure?
Are you trying to say that pressurizing the cabin isn't necessary, so long as air temperature is maintained?
You understand that the entire cabin air supply is constantly being replenished, and every few minutes the entire cabin air is completely replaced is a constant, ongoing proces...correct? Air is constantly being pumped in, constantly let out, and it's conditioned on an ongoing basis to maintain a comfortable and safe temperature.