Hello, expert solarpunk here.

TLDR: Car battery is 350Wh. Fridge uses 143W idle, so it’ll run a fridge for 2-3 hours.

Explanation below:

Car batteries are lead-acid (sulphuric acid and lead plates).

They discharge according to Peukert’s Law as the negatively charged plate gets covered in lead via the acid (electrolyte).

As the battery depletes, the negative plate can begin to take permanent damage, and so you can’t discharge a lead-acid deeper than 10-20%, or about 10.8V, with the safe limit being ~50% discharge.

Most 12V, 60Ah batteries therefore only safely store and nominally discharge 350 Wh @ 350W.

You can discharge that as fast as you want but the faster you discharge, the lower the capacity is (with 1000-1500W bringing you way down to like 65 Wh). Fridges have a surge when they start up to fire up the compressor. Starter batteries can take that, but once the refrigerant is cold, the fridge just maintains the temperature which uses a lot less energy - about 143W on average.