Well a basic arduino board draws about 50ma for it's own uses, so maybe 140 hours from that battery. But I suspect you may be powering other external devices and components that draw power from the arduino +5v pin or directly from the +12vdc battery? If so that current consumption would also have to be factored in to get a total battery run time estimate.
I had not thought of how I am going to power the other devices (specifically the Xbee) but the plan I believe was to use the battery to power the arduino, and then the arduino to power the Xbee.
It's not clear to me from this, but I assume the overheating problem is on the 5V regulator on
the Arduino board, due to its dropping a full 7V when the 12V battery is used.
7V * (whatever current is being drawn) = Pd, the power-dissipated in the v.reg.
For tiny SOT223 v.regs used on Arduino boards, Pd can be only .3W or .5W before the regulator
starts getting really hot. So, that means current in the range of only 50-mA or so before heat
starts rising. XBees and XBee Pros draw a lot more current than that when transmitting.
As others mentioned, linear v.regs are not very efficient. As you mentioned, 9V batteries
like the little 1" sized things, won't run your system for more than a few minutes.
Short of going to a switching regulator, I would try a series-R rather than a voltage divider,
pre se. With a full v.divider, the resistor going to ground will suck your battery dry in no time.
Rather just try using a series-R alone, with 4-5V being dropped in the resistor. Then, the
series-R will get hot instead of the v.reg, and that's a much better deal.
4V/.250Amp = 16 ohms or thereabouts. It needs to be at least 2W size.
You're still wasting a lot of battery in the series-R, as compared to using a switching
supply, but at least it should work.
I would just get one of there:
DC-DC adjustable switching regulator module.
Or one of these if you'd like to get it sooner rather than later.
I thought I didn't need any kind of converter now? I can just plug 12v into Vin and negative to ground right?
Your battery is 7 Amp hours, which means that it can more or less deliver 7 Amps of 12 Volt power for one hour. You should have plenty of power for what you want to do.
Let me give you some figures.
I looked up the XBee and XBee Pro. They take 50 mA and 300 mA (respectively) of 3.3 Volts. The Arduino will take about 50 mA of 5 Volts.
Your battery will provide 84 Watt hours of power.
So if you use two relatively high efficiency switching voltage regulators (one to give 5 Volts to run your Arduino and one to give 3.3 Volts to run your XBee), in theory the XBee will take 165 milliwatt hours, the XBee Pro will take 990 milliwatt hours, and the Arduino will take 250 millwatt hours. So the XBee/Arduino combination will run for about 200 hours, and the XBee Pro/Arduino combination will run for about 65 hours.
Even if you just use linear voltage regulators instead of switching regulators, you should have plenty of power. The XBee/Arduino combination will run for about 70 hours, and the XBee Pro/Arduino combination for 20 hours.
We are going to use Xbee Pro and Arduino Uno. These calculations are accurate to just plugging into the Vin and ground right? Without any kind of converter? 20 hours is more than enough if this is true. Also, if your saying this will work for 20 hours, we ALSO have a camera/camcorder wired with the same battery but it is only for convenience and doesn't look like it will be a problem with 20 hours of power.