True or False? Two identical beakers of water that have been over the same size flame for the same length of time will ALWAYS stay at the same temperature, no matter how much water is inside.

I don't think this is a true statement. Suppose both beakers start at 25C and we start the burners. It will take longer to heat the larger amount of water to boiling than it will for the smaller amount of water; therefore, the rate of heating will be different and the temperatures must be different with time. After both start to boil the temperatures of each will stay the same.