Humidity inside a closed hard case

Let's say environment is friendly toward a solid wood ukulele. So let's assume 68 degrees F and humidity is 45%. You take that ukulele and put it in its case and close it tight. And leave it that way.

What happens to the humidity inside the closed case? Does the wood absorb moisture and lower it? How sensitive is it to small temperature changes? Assume conditions in the room stay the same... does the humidity inside the case reflect this 45% or does it changed due to the closed environment?

I am assuming that NO humidifier is placed in the case. And (finally!), if the humidity changes for the worse, how many days is it okay to leave the case closed before opening it to breathe again?

I've wondered the same thing myself, but I doubt that it matters. Look at all the "vintage" ukes that we see around - for sale and in use. I doubt uke owners in 1925 had humidified cabinets and hygrometers to check on them. I think the air and moisture inside and outside a case will be so similar that any difference won't matter. If I can force myself to do this later, I'll put a wireless thermometer inside a ukulele case and see if the inner and outer readings differ. I'll have to find the sensor and the thermometer and get batteries for each, so don't hold your breath. : )

The humidity in the case should stay more constant than the room humidity, but it's (usually) not an airtight seal so it should gradually move towards the ambient humidity if there isn't a humidifier in it.