I have a 2007 Ford Mustang, 6 cylinder. A few hours after I drove it, the battery was completely dead. It can start with a jump, but if left to idle the engine stops soon after the cables are removed. I used a multimeter to check the battery, and when the engine is pushed to 2000 RPM, the battery jumps from 12V to 14V(pretty sure that means the alternator works). But once the engine is left to idle, it dies and needs another jump. Any help would be appreciated, thanks.
You can have a good alternator and still not charge the batteries if the connections are corroded in anyway or a battery clamp is loose or cracked. Also check the fusible links there should be one in line between the alternator to starter to battery circuit but if its pumping out 14 volts at 2000 rpm and wont idle for long afterwords then i suspect the voltage regulator in the alternator. To check this connect a voltmeter positive to the output post on the alternator and the voltmeter negative to ground, rev the engine up and down and watch the voltage output , if it fluctuates all over and intermittently then the voltage reg is the issue. Check the battery voltage at engine stop and if its the same voltage at idle then its the voltage reg or some other issue inside the alternator.
Normally if alternator is good, car won't die even without battery. I suspect alternator. I suggest you to buy a battery charger and charge battery and buy a Solar BA7 tester to test how many CCA are left in your battery. After eliminating battery problem, go ahead and buy an alternator.