I have a 50-gal Rheem tank with two themostats. Are both to operate at same time? I replaced both elements and upper element very coated but lower clean as if not operated very much. If not to operate same time, what situations will the lower kick on?

If your top element is bad the the lower element will never turn on be cause the top element completes the 240 circuit. It is like a resister in a circuit. Make sure top element measures out at 13 ohms.

Look on label on side of tank.
Wattage of tank will be element wattage. This is true if tank has one or two elements since both elements are never ON at same time.
Simply go to hardware store and buy 3500W element.
Take phone photo to store if needed for identification.
http://waterheatertimer.org/How-to-replace-water-heater-element.html
Wattage appears on end of each element.
http://waterheatertimer.org/How-to-test-water-heater-element.html
http://waterheatertimer.org/images/Voltage-printed-on-element-.jpg

It's probably bad upper or lower thermostat.
BUT... new element could also be shorted.
OR ... original tank is rated 1500 watt elements look at label on side of tank.
I always replace both thermostats to save time.
Lower thermostat costs $10 at Lowes.
http://waterheatertimer.org/How-to-replace-thermostat-on-electric-water-heater.html

Add a comment for more free help.
Also take advantage of fixya phone service.
For a price, expert speaks with you over phone while you work on heater or any do-it-yourself project.
Fixya is always less expensive than a service call.

You have electric water heater.
Electric water heaters are fully repairable by homeowner, excluding hybrid type.

Rheem electric water heaters:
http://www.rheem.com/products/tank_water_heaters/electric_water_heaters/
Rheem fury series manuals and models
http://www.rheem.com/product.aspx?id=09DF2BDD-5E11-4D32-B574-84ACFB8A4619

Age of Rheem water heater is first 4 digits of serial number located on side of tank: for example 0705 means July 2005.
Serial number also shows model number & wattage of elements.

A) If your water heater receives very cold incoming water, it may not heat fast enough to keep tank warm.
Add a tempering tank.
http://waterheatertimer.org/Tempering-tank.html
Add insulation over entire water heater except TP valve. Insulate pipes completely.
Read more information:
http://waterheatertimer.org/9-ways-to-save-with-water-heater.html

B) If cold outside temperatures are not to blame, your water heater may have a bad thermostat or bad lower element.

C) 40 or 50 gallon water heater is 240Volts and tank will have 2 access panels on front.
Rheem ships all water heaters with 4500 Watt elements.

Narrow down the suspects:
D) Water heater has some hot water.
This tells us upper element is working.
And that water heater electricity is working.
And that reset button is not tripped.
And that heater is not experiencing run-away overheating event.

That gives us 3 solid suspects.
1) lower element is burned out. Test lower element using inexpensive multi-meter from Home Depot.
http://waterheatertimer.org/How-to-test-water-heater-element.html
Replace element with same wattage shown on label, and clean out sediment:
This will restore water heater to full 99% efficiency.
http://waterheatertimer.org/How-to-clean-sediment-out-of-electric-water-heater.html
http://waterheatertimer.org/Clean-sediment-out-of-water-heater.html

2) Upper or lower thermostat is bad. Replace both thermostats for about $25.
http://waterheatertimer.org/How-to-replace-thermostat-on-electric-water-heater.html
If you want to test thermostats and all parts before replacing anything:
http://waterheatertimer.org/How-to-troubleshoot-electric-problems-with-water-heater.html

3) Burned or shorted wire. Turn off power. Open covers on side of tank. Remove insulation. Inspect parts for signs of high heat and burning. Especially lower element. Tighten any loose wires. Replace part that shows signs of burning.
Put insulation and cover back over thermostats so cooler outside temperature doesn't cause thermostat to misread tank temperature.
Rheem element

Your testing may be off here. Or you might have special order 'simultaneous' wired water heater.

Water heaters with two elements are 240V.
Elements test for 120V at all times, but with ordinary non-simultaneous water heater, only one element at a time has 240. This is called non-simultaneous operation.
Open links below for understanding of water heater operation.
http://waterheatertimer.org/How-it-works.html
http://waterheatertimer.org/How-water-heater-thermostats-work.html
http://waterheatertimer.org/B220C.html

If both elements were drawing 240 at one time, then upper thermostat is bad, or else your water heater is wired for simultaneous operation, and one of the elements is burned out.
http://waterheatertimer.org/How-to-test-water-heater-element.html
Your tank might be wired for simultaneous operation, if water heater was special order from Rheem, or if somebody changed wiring and set lower thermostat-and-element on a separate circuit breaker.

If you have simultaneous operation, then you would have 2 circuit breakers and 2 wires going to water heater or one 50 amp breaker with 8 gauge wire to heater. If this is the case, then both elements could test for 240V and one of the elements is bad, and thermostats are ok.

If you have ordinary Rheem water heater, then it is wired for non-simultaneous operation where only one element is ON at a time. This is called non-simultaneous operation and you can check because water heater has one circuit breaker rated for 20 or 30 amps.

Rheem elements are 4500Watts.
If both elements were ON at same time, that would be 9000Watts, which would trip typical water heater 20-30 amp circuit breaker.
9000Watts divided by 240 volts = 37.5 amps
So if upper thermostat is bad, and it is turning on both elements so they both test for 240, then thermostat is bad, but also one of the elements has to be bad.
Or test is inaccurate.
Interesting puzzle.

Add a comment for more free help.
Also take advantage of fixya phone service.
For a price, expert speaks with you over phone while you work on water heater or any do-it-yourself project.
Fixya is always less expensive than a service call.

http://www.rheem.com/product.aspx?id=09DF2BDD-5E11-4D32-B574-84ACFB8A4619
http://globalimageserver.com/fetchDocument.aspx?id=052c9e32-ce37-48d7-8990-9e430f23fef3

82V80-2 Energy factor is .86 according to water heater industry self-regulated standards.

Rheem pdf says these water heaters are wired for non-simultaneous operation.
Except special order water heaters.
Non-simultaneous operation uses single 240V circuit as described below.
If your water heater is wired for simultaneous operation, and each element is on a separate circuit, that makes your water heater special order. I would guess the reason is for higher first-hour delivery, which implies rapid heating and would likely affect energy factor.
You might want to get serial number off model and call Rheem for specs on that special order.

Your water heater energy factor may be the same because 'energy efficiency is based on the amount of hot water produced per unit of fuel consumed over a typical day.' This means an aircraft carrier can be considered highly efficient despite overall cost. And naturally the guys making the aircraft carrier are also doing the rating.
http://www.energysavers.gov/your_home/water_heating/index.cfm/mytopic=13000

Non simultaneous operation means the upper thermostat controls heating functions.
240V goes to upper thermostat first.
When water inside tank is cold, thermostat reads temperature through tank wall.
Upper thermostat turns on upper element until top 2/3 of tank reaches thermostat set point.
Once set point is reached, upper thermostat turns off upper element and sends power to lower thermostat and lower element.
Lower thermostat reads temperature through tank wall, and turns on lower element until bottom 1/3 of tank reaches thermostat set point.
As water cools inside tank, lower thermostat is first to respond since hot water rises.
Lower thermostat turns on lower element until tank again reaches set point.
When hot water faucet is turned on, hot water exits top of tank.
At same time, cold water enters bottom of tank through the dip tube.
The heating cycle repeats.
At all times, the electricity flows through upper thermostat. And upper thermostat is powered by one 240V circuit.

With simultaneous operation, the upper and lower thermostats work in same manner.
Except thermostats are wired separately.
Lower thermostat does not wait for upper part of tank to be heated first.
Lower thermostat turns on whenever lower part of tank cools.
The advantage is more hot water available rapidly when demand is high. This is called first hour recovery.

One method for reducing electric consumption is to set lower thermostat so it only turns on during certain times of day. For example Whirlpool Energy Smart operates in this manner and shaves a few bucks off the bill each month. This says that simultaneous operation is not an energy saver, unless that circuit controlling lower thermostat is set on a timer.

Lower element can be burned out and still read 230V across screws

1) We know thermostats are working because elements test 230V.
2) We know upper element is working because tank has some hot water.
If upper element is burned out, tank will have no hot water.
http://waterheatertimer.org/How-it-works.html

3) Here's how to test lower element:
http://waterheatertimer.org/How-to-test-water-heater-element.html

4)Here's how to replace element
Rheem element is 4500Watt bolt-in type
http://waterheatertimer.org/How-to-clean-sediment-out-of-electric-water-heater.html

5) Rheem manual says: Heaters furnished with standard 240 volt AC, single phase non-simultaneous wiring, and 4500 watt upper and lower heating elements.
http://waterheatertimer.org/pdf/Rheem-spec-sheet.pdf

Rheem 4500Watt element

yes bottom 1 bad

did you turn the power on BEFORE you filled it with water???

this is a pretty common mistake. you will need to check the upper element to make sure its working.
most water heaters have an upper and lower themostat. the upper thermostat is the one we need to check.

use your volt meter...

turn the power off, test with your volt meter to make sure! remove one wire from the element, not the thermostat, and check resistance on the element. if no resistance, you burned the element, and will need to replace it.
replace with same wattage, usually 4500watts. it will be written on the element.
also, I like to push the reset button on the thermostat to make sure it wasn't tripped.

You can eliminate the shower control knob possibility by turning on your hot water anywhere else in the house. If you get hot water in other places, then it could be the knob causing it. A substantial lime buildup in the tank can also cause poor heat transfer from the elements to the water.