Replacement element part # for 83VR52-2

first off , it is probably a genuine hot water system
secondly --- the heating elements are not made by the manufacturer but are off the shelf items that are made by electrical manufacturers as this reduces the cost of the unit and allows spares to be bought any where from reputable dealers or plumber shops.
that would explain why there are different elements as they may have failed at some point and have been replaced by a plumber
next , it doesn't matter which element is positioned where as they head water and the location , being in close proximity would not make a great deal of difference
normally there would only be one element in operation as the extra element is for fast hot water recovery ( long hot showers , many people showering or fast heating after all the hot water has been drained for an element replacement)
the element with all the controls would be the main element and it will control water temperature and also it should have an adjustable screw or knob , that can be turned to adjust the thermostat setting
there should be wires to the second element from the controller of the main element so that it is cut in when the water falls below a set temperature
If you have 25 years and the system is not leaking anywhere then the cheapest outcome is to have an accredited electrician/ plumber check out the elements
The secret to hot water systems is to have the thermostat setting low ( around 65 degrees c is hot enough for the hands and body) and the temperature difference between utility supply temperature and the set temperature means that you can draw off more water before the hot water system switches on the power
conversely if you have it set so that is at 100 degrees C the the cold utility supply only has to drop the water 10 degrees and the power switches on to maintain the 100 degrees C
any way get an accredited electrician / plumber in to check it out and get a quote

Is their not two elements, one at the top too? If it is tripping on the high limit switch it could be the thermostat Try checking the grounding of the unit.

. http://en.wikipedia.org/wiki/Residual-current_device

To check to see if it is a bad element - turn the power off again and use a multimeter to check continuity (Ohms) in each element. It is not uncommon to have one element fail. Replacing an element is "elementary" :), if you have some mechanical aptitude. Just be sure and drain the tank to below the level of the failed element. Easier if it is the upper element of course. Again - be sure the power is OFF - check it with your meter before you begin and you may even want to lock out the breaker if there is any possibility of someone mistakenly turning it back on.

The Rheem water heater uses 4500 Watt elements
Check label on side of any appliance to see electrical rating details
2 element tank with two 4500 watt elements is still a 4500 watt appliance since both elements are never ON at same time.

Volts x amps = watts
amps = watts divided by volts

amps = 4500 divided by 240Volts or 220Volts
amps = 18.75
Your water heater uses 18.75 amps to 20.45 amps

Your 25 amp breaker should only carry 80% of rated value
25 amps x 80% = 20 amps.

So your water heater breaker is correctly sized.
You should have a 10 gauge wire going to this water heater.
12 gauge wire is a bit undersized for 4500 Watt water heater
Feel the water heater wire to see if it is warm.

If the main breaker is getting hot when 20 additional amps are being used by the water heater.
1) The house is using more amps than your 100 amp main can carry
Using the formula, 100 amps x 80% = 80 amps for the main breaker
Add up your total amp draw.
For example if your 3500 watt oven is ON, it draws 16 amps.
If your 5000 Watt electric heater is on, it draws 23 amps.
Your 1500 Watt 120V microwave draws 12.5 amps.
Add these numbers up plus your water heater, and it comes to 71 amps.
71 amps is getting close to the max 80 amp, but it's not over.
Now if you have a pool pump and and hot tub and a table saw going, the main breaker could be overdrawn.

2) To solve the problem short-term, you can put a timer on the water heater and use it only when needed.
http://waterheatertimer.org/Compare-13-electric-water-heater-timers.html

3) The main breaker is bad and needs to be replaced.

If you need help figuring circuits or timers, add a comment and I will help

If you're having to reset the breaker, then most likely you have a bad heating element. Usually the bottom element burns out first, however if you had the water off, and the level dropped in the tank, the heater might have come on without water in it. This will cause it to overheat and burn out. Now when you turn the breaker on, the current is going to ground, tripping the breaker. If you are handy you can replace them, but be sure water heater electric is off or disconnected, and then drain water below the element level. While you're replacing one element replace them both.

Check the breaker and top thermostat and make sure they are not tripped. Move onto replacing elements if above is not the problem.
Turn water and power off to heater and attach a water hose to bottom of heater to drain down tank. May have to open hot side on a facuet to get it to drain.
Once drained remove elements with 1 1/2" found at local hardware stores. once elements removed and new ones in place. Turn water on and get the air out of the system. Once water is flowing from the hot side from all of facuet's in house.
Once all air is out now yaou are resady to turn power onto heater.

It is probable a lime build up in the bottom of the water heater tank. You can remove the bottom heating element and clean the lime out, keep in mind this sometimes turns into quite a job though. And you may damage the heating element during removal and have to purchase a new element.

Have you checked to make sure that the elements are good by checking the ohms. Be sure that the power is off and the wires are disconnected from elements and then also be sure to check the ohms across the tank to make sure there is not a dead short in the element reading through the tank. If both elements are good then I suggest replacing both thermos then they will both be new and should work for you . Thermos can be problematic when trying to test them sometimes they won't always give you correct readings. Make sure you have the breaker off whenever you mess with a waterheater, and make sure you install the thermos correctly with the right wires going where they should.

It's possible that the tank wan't full when the elements were on. If the elements aren't completely covered with water, they will burn up. You need to check the ohms on the elements. They should read between 5 and 10. If they are fine, then the thermostat is bad on it. They are real easy to replace.