Is having to open the regulator up after chilling normal?

I just kegged my first batch this Saturday and I have a question.

Beer temperature was about 40 degrees when it went in the keg. Both the keg and the CO2 bottle were at room temperature. I filled the keg and set the pressure to 30 psi for half an hour to set the O-ring then turned the pressure down to 12 psi and placed the keg and CO2 bottle in the fridge. The keg regulator was reading 12 psi. When I checked on the keg Sunday morning the regulator gauge was reading 0 psi. I opened up the flow on the regulator a bit and a little gas flowed into the keg and everything was back to normal. Later in the afternoon I checked it again and the pressure was down to about 10 psi. Again I opened up the regulator to get it back to 12 psi. This morning I checked it and it was reading 12 psi.

So my question is...Am I correct in assuming that I had to adjust my regulator a couple of times because the gas was cooling and thus lowering the pressure in the system?

Thanks.

Yep. It's from putting the CO2 tank in the fridge. PV=nRT I believe would explain it. Temp (T) drops, Volume (V) stays the same, therefore pressure (P) must drop. Science is magic!

I understood that the pressure was going to drop on the tank and the keg, I just wasn't sure if I should have to play with the regulator flow because of it. It kind of made sense that I might but I thought I would just check to put my mind at ease.

PV=nRT...Been a while since I have seen that formula.

Thanks.