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I am totally new to having a RES. I have a 4" RES in a 20 gallon tank. 3" of water on one end and a sloped beach (play sand) on the other. My turtle stopped eating 2 days ago and buried himself in the sand and does not move. What is going on and what should I do? Based on the short front claws, I think that it is a female. (never found any eggs though)

It's likely too cold. You absolutely need to have a submersible water heater... around 76F is a good temp to set it at, +/- 2F won't hurt.

Also, you'll need a lot more water as heaters are not really made for low water levels.