Can the capacity of a battery be determined from Volts, Amperes, and output of Joules for xyz amount of time?
Normally the capacity of battery is specified by "Watt-Hour" written on the battery or in the battery datasheet. If this isn't specified, "Amp-hour" will be written on it.
You can calculate watt-hour using this:

Watt-hour = Voltage x Ampere hour (specified on the battery)

E.g Battery voltage = 12v , Amp-hour=1000, then

watt-hour = 12 x 1000 => 12000 watts-hour.

what this means is that if the battery supply 12000 watts to your car/circuit, it will work for 1 hour (ideally though).
1 watt = 1 Joule/sec; so 7000joules/3sec => 2334 watts.

It means that it can supply ~2.3KW to the load. Now if you want to calculate the operating time of battery for a specific load, say, 200watt load, 
watt-hour/watt(load) => 12000/200 =>60 hours (theoretically)