So does the battery go dead while its running or while its shut off?

Whike its driving.

While its driving. I used a volt meter on the new battery and it read 12.5 volts. I turned the car on and it jumped up to 13.9 to 14 volts. When the idle changed after 15 min with the volt meter still attached the power dropped to about 12 volts and the battery and oil light on the dash turned on. Then the idle changes back and the volts start climbing again. Now I'm afraid to drive it because when I do drive it and the idle changes the power will go down to 10 volts and all the Gage's start going haywire. The car will hesitate then die. I put in the. New alternator and new battery two days ago, so both are working perfectly. While its parked and running is when the drain happens. I haven't really driven it since I installed the alternator and battery, I just let it run while it's parked until I figure out what causing the Volts to drop

So the new alternator does the sane thing as the old one?

Yes

i would start by verify powers and grounds at the battery and then look at the connectors at the alternator.

Roy

I would do that when the charge voltage goes down bellow normal.It might just be a loose wire somewhere.