Agree with both responses except the voltage number. The actual voltage will depend upon the rpm being over idle, like 1000-1500 min to get the alternator output up to regulation voltage and then increase at a very slow rate, and the charge level of the battery. The alternator has an output current limit and if that is exceeded it limits the current which limits the voltage across the batt terms. Once the charge is near max, the alternator voltage regulator will set the output voltage near the max regulated value with the reduced current.....the regulator has a wattage rating and will contain the volts and amps to remain in that envelope.
I am currently accustomed to alternators on marine outboard engines but they use the same batteries as other things and the "rules of engagement" should apply. The number there is 14.5v max for a regulated power source and 16+ for unregulated.
Wet cell batteries use a mixture of Sulphuric Acid and water to accomplish the chemical transition with the lead plates as a function of power moving in or out. The Sulphuric acid remains in the battery normally, but the water boils out at a lower temperature and since they are dissolved in solution carries some acid (H2SO4) with it which is extremely corrosive.
The charging rate determines the amount of boiling and the temperature of the battery. High charging rates generate visible bubbles which is the water boiling out. The higher the charging rate the more bubbles, the higher evaporation rate which lowers the water level in the battery. On older style non "maint-free" batteries there are caps on the battery (such as what I see in your picture) which can be removed and the process monitored, including the water level.
On your battery with the observed overflow, I would expect that the solution level would be well below the "full" ring and possibly low enough to expose the tops of the plates.
A few checks could tell you what you want to know, as listed above but shooting from the hip, I'd say that your regulator in your alternator isn't regulating and that is something that your dealer is obligated to repair/replace.
The other possibility is a defective battery with a shorted cell, very unlikely at that age of usage, which causes the alternator with proper regulation to continue to pump current into the battery in an attempt to get the terminal voltage up to the point where the alternator shuts down the current. A load test of a fully charged battery could answer this question. First off would be the terminal voltage. If the battery has sufficient water to reach the full rings and has been charged, but has been off the charger for at least 12 hours the terminal voltage should stabilize at some value within the 12-13 volt range.
With that you connect the battery to a load tester and crank up the current to 200 amperes. A good battery will hold approx 11v at the terminals. Most battery testers have 2 meters (current and voltage) with green, yellow, and red scales. The scales tell you what to expect for the applied load. Wally World has them in the auto service bay.
Once you have your battery tested, if it passes and hasn't been "killed" you are ready to approach your dealer to fix his tractor's regulating system and while he's at it he can add cleaning up the collateral damage to the effort.
New batteries just don't do what you are seeing for no reason and on a new battery, usually it's not the batteries fault.
HTH,
Mark
