How long is a string? Pretty much what you have asked. You didn't tell us what refrigerator (how much power it uses), how many batteries are available for running the fridge, how hot is it inside the RV, how many times is the door opened and for how long, what other devices can draw on the same batteries as the fridge, etc. etc.
The better rigs typically dedicate at least 2 and sometimes 4 largish batteries to a residential fridge with its own inverter to drive it. Let's say there are 4 GC2 batteries for a total of 450 AH, dedicated to the fridge and its inverter. Those can produce about 5400 watt-hours of power. Losses in conversion reduce that to around 5000 watt hours, and battery life considerations mean that only about 50% of that is available. Let's say 2500 watt-hours are left. According to fridge rating tests, a typical new residential fridge can probably operate for a full day on about 1400-1800 watt hours, but that is rather conservative usage. By that I mean the room is relatively cool and the door is not opened very often. The numbers change swiftly if those factors are changed.