[OTI]

So the problem goes like this:

Large trucks on steep hills usually shift their engines into lower gear to slow themselves down. Where does the kinetic energy of the truck go when they do this?

Just a note before I start with my thoughts, I'm just going to say that I learned thermodynamics for the first time today and I only learned the first law so forgive me if I am making a fundamental mistake.
Now, after researching about how car gears work, I'm just going to assume that they work similarly to bike gears. High gears are bigger and give more power (I guess) while low gears are smaller and take more to get more.

I'm kinda unsure about the transitions between types of energies, but I'm guessing the energy somehow goes into the input, counter, and/or output shafts and maybe the dog clutch in the form of potential energy because the shafts and clutch might be stressed because the output shaft is trying to go at a higher rpm than the other shafts.

That's all I have. Would be glad if I could not only get the answer, but help in transitions in energy. Thanks.

[Borek]

I'm guessing the energy somehow goes into the input, counter, and/or output shafts and maybe the dog clutch in the form of potential energy

There is no way they can store potential energy in such amounts.

However, the mechanical transmission system transfers the energy into the engine, forcing it to rotate. Do you know how the engine works and what it will do when it is forced to rotate without fuel?

[OTI]

I'm guessing the energy somehow goes into the input, counter, and/or output shafts and maybe the dog clutch in the form of potential energy

There is no way they can store potential energy in such amounts.

However, the mechanical transmission system transfers the energy into the engine, forcing it to rotate. Do you know how the engine works and what it will do when it is forced to rotate without fuel?

I have no idea actually.

Also, I watched this video: https://www.youtube.com/watch?v=wCu9W9xNwtI

Does the kinetic energy turning into friction through the synchronizer ring sound possible?

[Borek]

I have no idea actually.

Also, I watched this video: https://www.youtube.com/watch?v=wCu9W9xNwtI

Does the kinetic energy turning into friction through the synchronizer ring sound possible?

No, it is not about mechanical parts of the engine.

Take a look here:

https://en.wikipedia.org/wiki/Four-stroke_engine

Two of the cycles are idle - they neither consume nor produce energy (well, almost, they consume a bit, but we can safely ignore it here). What about the other two?

[OTI]

The Intake stroke produces energy as it increases the potential energy of the system, assuming that the system is the engine.
The Compression stroke is an idle stroke if you disregard the energy needed for it to happen.
The Power stroke could be said to be an idle stroke as the amount of energy in the system not changing (I think, cuz the potential energy is just being transformed into heat energy (If that is possible))
And the Exhaust stroke should release the heat energy made in the previous stroke from the system.

Is this right?

Looking back at my question, I can only see the kinetic energy of the truck being made into heat energy by friction through the mechanical parts of the engine and/or the gears unless the energy was put towards driving the intake stroke. Or maybe it's both?

[Borek]

The Intake stroke produces energy as it increases the potential energy of the system, assuming that the system is the engine.
The Compression stroke is an idle stroke if you disregard the energy needed for it to happen.
The Power stroke could be said to be an idle stroke as the amount of energy in the system not changing (I think, cuz the potential energy is just being transformed into heat energy (If that is possible))
And the Exhaust stroke should release the heat energy made in the previous stroke from the system.

I would say it is exactly the reverse.

Intake and exhaust are just moving the gas, so they are mostly idle, compression requires a lot of energy to squeeze the gas (piston does the work on the gas), power stroke is where the energy is being produced and combustion products do the work on the piston.

But when you are using the engine to slow down the car you are not supplying the fuel, so the power stroke doesn't exist.

Ideal engine, with ideal gear mechanism, would just compress the gas and then the compressed gas would do work on the piston, so that the energy balance would be zero - as much as was put in would be put out. But the engine is not ideal, and it gets hot in the process, both because of friction and because the compression and decompression are not entirely adiabatic.  And yes, you are right in the end it is the heat energy.