Today I accidentally left my Hyundai i30's headlights on for two hours.
When I tried to start the car the battery was very weak at first and I had no power in acceleration.
Then I turned off the car and restarted it. I drove it around the block a couple of times and seemingly it was at normal power.
What should I expect when I turn the car on tomorrow? Is it likely that I've caused permanent damage to the battery?
If you got a low point discharge, your battery is damaged. Some chemical processes can not be reconverted from that point. If you drive around for some time, your battery will get warm and have a little bit more charge then cold. That could be enough to start the car once again. You don't loose anything if you try to charge you battery. Maybe you are lucky. Otherwise if your car does not start tomorrow, you will need a new battery.
UPDATE:
The border for deep discharge is about 20% of the maximal charge. If you reach this level ( under 20 % ) a lot of lead was resolved in acid and your pH-value decreases. That brings you a sulphation of the active mass and causes a capacity fade. Your plates corrode. Lead sulfate becomes crystalized and can not be transformed to acid anymore.
It depends on how deeply-discharged the battery was. If the battery is high enough capacity two hours may not harm it.
Starter batteries (used to start automobiles) are designed differently from deep-discharge (or "marine") batteries. (For traditional flooded acid batteries) starter batteries are designed to provide lots of current to turn an engine, and as such the lead plates are more like a mesh to maximize contact area with the acid. This also means that the more you discharge it, the more the plates disintegrate. Starter batteries do best if never discharged too much. (Deep-discharge batteries cannot provide large amounts of power quickly but can be drawn on until almost empty - their plates are solid and do not disintegrate as much if drawn close to empty.)
Normally the alternator of a vehicle generates enouogh electricity to both charge the battery (if the engine RPMs are high enough - idling isn't enough) and fire the spark plugs. If the car won't start reliably the next day (assuming you drove around at a moderate speed for some time) then the battery may be damaged.
If you are concerned, best to go to a mechanic who can load-test the battery with proper testing equipment.
There are some pulsing chargers that claim to reverse sulfation but they typically cost much more than ordinary chargers.
Leaving the headlamps on for a couple of hours will not do any signicant damage to a car battery. Re-charging the battery overnight would normally put it back to fully charged. 'Smart' alternators used on todays vehicle will also charge your battery. When discharging, the plates of the battery become sulphated. Charging the battery removes this sulphation. If the battery grids and plates are not physically damaged, a charging and discharging of the battery many times over at a very low amperage will recover any battery. In theory you only ever have to have one battery for the life of your vehicle. The time and effort required to recover a very sulphated battery is not really an option when compared against a simple replacement.
Generally batteries that are damaged from excessive discharge will be protected by a discharge monitoring circuit that prevents discharge beyond a certain point, however these circuits themselves draw a small amount of power, which means that even with such a circuit, a battery could be damaged if left undercharged for an extended period of time (weeks, not just a single day).
Your battery should be fine, however driving it around the block may not be much RPM for the alternator to charge the battery back up - Ideally you would charge the battery with a battery charger, however you could also put the car in neutral with the engine on, hand-brake on, and let the engine run at 3000 RPM or so for a bit.
You've done SOME damage, but probably not a great deal of damage. You've shortened your battery life somewhat by contributing to its sulfation.
Some irreversible sulfation is inevitable in lead-acid batteries. Some is reversible, some is not. The deeper a (lead-acid) battery is discharged, the greater the amount of irreversible sulfation.
Part of the problem is that lead sulfates are fragile, and drop away from the plates, building up as conductive sludge at the bottom of the battery. If it builds up high (deep) enough, it'll short-circuit one cell and your nominal 12V battery will irreversibly become a nominal 10V battery.
The chargers that claim to remove sulfation have some limited capability of doing so, but not to any great degree. I see them as a waste of money - they may increase the battery's expected service life of seven years to eight. Or to seven and a half. More likely, if used often, they'll overcharge a battery and result in boiling off some of the liquid that you can no longer replace because your battery now has no refill caps. In the old days, we could add distilled water or battery acid, whichever was lacking at the time (depending upon the charge state), and adjust the battery's specific gravity to ideal at the fully charged state. We even had the capability of washing the sludge out of the bottom of the battery, if we were adventurous. Yes, I've done it. Now you have fewer items on your menu - you've traded your freedom for security.
Tomorrow, provided your drove your car for some fairly decent distance today to recharge your battery, your car should start normally... unless it was already in its last six weeks of life. Doubtful. Someday you'll need to replace it - that day will be earlier than it could have been, because of your discharge, but you probably won't notice. You probably won't even remember this event by that time.
