Sure, let's say you have a typical car battery with a capacity of 60 amp-hours (Ah).
And let's assume you have a small refrigerator that consumes about 100 watts of power when running.
To calculate how long the battery can power the refrigerator, we need to convert the power consumption from watts to amps.
Power (watts) = Voltage (volts) × Current (amps)
Assuming a car battery voltage of 12 volts:
100 watts / 12 volts = 8.33 amps
Now, we can determine the approximate runtime:
60 amp-hours / 8.33 amps ≈ 7.2 hours
So, with a fully charged 60 Ah car battery, you could run the refrigerator for approximately 7.2 hours before the battery is completely drained. However, it's important to note that factors such as battery age, temperature, and other loads on the battery can affect actual performance.
If your dome light isn't an LED, then you should replace it with one. It won't completely fix your problem but it will give you 9 to 10 times longer to catch it.
There's really no reason that every car doesn't have a voltage cut off to protect the battery such that it can still start. Additionally, if they just included a super capacitor then even with a heavily discharged battery, it could charge up the super capacitor to then start the car.
But if we went around doing smart stuff like that then we could potentially wreck the entire lead acid battery industry and that would just be awful...
if the car was running, the alternator would be charging the battery. would it be able to keep up with the drain of the fridge of just extend the time a bit?
Probably depends on the car + alternator, but it's not so rare for modern gas cars to have AC outlets for backseat passengers, and the ones I've seen are typically rated 120-150W or so. Glancing at the power meter I have on my fridge, it uses ~110W while running and only runs ~10% of the time.
Theoretically the car probably can keep up while running, BUT
Compressor startup current may blow whatever fuse is protecting that circuit.
AND
Cars are very inefficient generators. You'd be wasting a bunch of fuel so I wouldn't generally recommend it unless it's an emergency.
That said, in an emergency it may be worth doing for like 20 min on / 1 hr off, so that you're running the engine only when needed, but I'm not an expert, that's just pure speculation.