Thank you all but i am confused.... i had not so many time to read in depth all the comments but here are some things that will make you life easier
My supply will be a 12 volt 1 amp ac to dc converter
I only need 1 channel (left or right ) or even both no prob.
I need adjustable gain with caps or resistors
I need it to be loud but no so easily distorted
As for heat dissipation its ok ill use a big ass heatshink or even combine a small heatshink with a fan for maximun cooldown
Ok, Chris, here's a very basic explanation.
Amplifiers output a certain amount of power (in watts) based on the resistance of the speakers ( in your case 8 ohms) and the input voltage they receive (and the current, naturally). Some audio amplifiers aren't that sensitive to input voltage, others are.
These amplifier chips that I mentioned (tda2040, tda2050) like bigger voltages a lot, the more voltage the more audio power they can output. With these amplifier chips, as you can see in the graph above, the power output increases quite a lot as you increase the input voltage... with +/-5v (10v with single power supply) you only get 2-3 watts, with +/-22v (44v with single power supply) you get 25-30 audio watts (ten times as much).
Other amplifier chips like the TDA1519 mentioned by madires only works with a smaller range of voltages and is a bit more efficient with lower voltages, but as a downside it can't give you as much power as the previous chips - it tops out at about 5-6 watts while the tda2050 can do about 20-25 watts.
The amplifier chips that can output a lot of power are usually designed to be used with split power supply. That is, you have a transformer with two secondary windings or a single winding with a center tap, and from that you can create a negative voltage and a positive voltage, so they amplifier has two input voltages, like this:
From top to bottom, you have at the output +V , GND and -V
In the picture above, you have a transformer that outputs 48V AC with a center tap - the center tap becomes the ground, and there's a positive 24v AC and a negative 24v AC. These are RMS values, so when converted using a bridge rectifier like in the pictures, you get about 34v. So that is a +/- 34v split power supply.
The TDA2050 can handle a maximum of +/- 25v so this transformer is actually too big for it, but it's just an example.
Split power supply is better for audio amplifier chips because it makes it easier for an audio amplifier to create the audio waves that are sent to the speakers.
Single power supply is the power supply like you have on the computer or on ac to dc adapters, where you have just ground and a positive voltage.
Some amplifier chips can work with just positive voltage but when using such power supply you have to keep in mind that the voltage difference is now half compared to a split power supply. 12v DC is equivalent to -6 - 0 - +6v split power supply because from -6 to +6 is a potential difference of 12v.
So wherever you look in graphs made for split power supplies, you have to look at the values for half the voltage for your single power supply.
Now, as the amplifier chip no longer has that positive and negative voltage, the output is harder to generate and it's a bit hard to explain but in such configuration a large capacitor is needed in front of the speaker - if you look in the datasheet for TDA2050 you will see the "single power supply" design has a 1000uF capacitor near the speaker while the split power supply doesn't need one. The TDA1519 works around this issue in BTL mode by making both audio amplifiers in the package work like a single amplifier so in that mode, the audio chip needs two speakers connected for each channel.
Going back to your original problem.
You have a 12v 1A ac to dc adapter. The power this adapter can deliver to some device is determined by the formula Power = Current x Voltage so the power for this adapter is P = 12v x 1 = 12 watts.
An ideal amplifier would take these 12 watts of power and produce 12 watts of audio power.
However, you have to understand that audio amplifiers are not ideal, and depending on their type,and they're not very efficient. The amplifier chips we're talking about here are class AB amplifiers, which usually are about 60-70% efficient.
But as you can see from that graph I showed you, with 12v input, the amplifier chip can only produce 2-3 watts of audio power without causing a lot of distortion, it just doesn't "like" such low voltages.
So you give it 12v, but produces about 3 audio watts. It probably has about 50% efficiency so the tda2050 probably uses about 6 watts out of those 12 watts you make available, the rest are unused. If you make two amplifiers, one for each channel, both chips will use in total 12 watts or more, so your 12v 1A ac to dc adapter is to the limit.
I originally told you about 12v because computer power supplies have 12v, so it would be easy to get a used power supply from a computer or just power the audio amplifier from your computer.
But keep in mind, even if you connect it to a power supply that outputs 12v and may output 20-30 A on 12v (250-400w), the audio amplifier chips won't use this power, because they don't like such low voltages, they'll still only use about 6-10 watts.
The beauty of these chips is that you use properly rated capacitors (with big voltage rating) you can power these audio chips from 12v and get only 3 audio watts in speakers and when you find a transformer you can replace the 12v with the output of that transformer and get lots of audio watts.
For example, let's say you find somewhere a 24v AC rms transformer rated for 50 VA (a new one costs about 15-20$, on eBay they're cheaper but shipping to Greece costs anyway money). When converted to DC, that 24v AC rms becomes about 32 volts. The total power of the transformer is 50VA, you can equal that to 50 watts.
If you go and look on that graph, 32V DC from a single power supply is equal to about +/- 16 V so the TDA2050 could produce about 13-14 audio watts in the speaker. Now keep in mind the amplifier chip is about 60-70% efficient, so to produce those 13-14w of audio power, the amplifier "eats" about 4-6 watts and wastes it as heat, so in total the amplifier chip uses about 20w out of those 50w the transformer can give.
So even though the transformer makes 50 watts available, a single tda2050 would use only about 20 watts. That's great, because you want stereo, so you basically have two identical circuits and in total, the two amplifier chips would use about 40 watts, which is below the 50 watts the transformer is capable of.
The gain of the amplifier... normally, you don't mess about with it, you just set it to a reasonable value (the one recommended in the datasheet and mentioned on that website with hi-fi amp based on tda2050) is a good one. You can always adjust the volume from your sound card. Either way, you can adjust that quite easily on a lot of amplifier chips.
The LM386 probably needs one because it distorts a lot otherwise... the lm386 is lousy for powering speakers like the ones you say you have.