It’s one of those cooler/heater things if you are wondering.
What run time can I expect off this before depleting the battery to a point where it could cause starting trouble and/or shorten the life of the battery?
For the sake of this, lets just assume a generic car battery, nothing super big, I don’t have the CCA or reserve capacity handy.
I believe the typical small car battery is rated at around 45 amp-hours. That means that it can theoretically deliver any combination of current and time such that
current X time = 45 amp*hours.
So, you could run a 1A load for 45 hours or a 45A load for 1 hour. In reality, heavier loads have associated losses that reduce the amount of time you can expect the battery to last.
A 4 amp load isn’t all that heavy, and that’s probably the peak load–the draw experienced when the fans and Peltier junctions are all pulling current. Practically speaking, you should probably get at least 10 hours out of a full charge. Past that, and you may get enough of a drop to starve the cooler’s power supply and make it drop out. (That happens with my cooler, but it’s an older model and may be a bit touchy.)
Did you mean to post this in General Questions?