For simplicity and to account for the most basic affects, we can use the ideal gas law which is as follows:
PV=nRT
where:
P=pressure
V=volume
n=number of moles
R=gas constant
T=temperature
The variables V, n, and R are constant for a cylinder of air that just changes temperature with the same amount of air in it. Therefore, we can say that P is linearly proportional to T (and vice-versa). When T increases, P increases linearly, and when T decreases, P decreases linearly.
You can also think of it this way: since V, n, and R are constant, we can re-arrange the equation so that P and T are on one side and V, n, and R are on the other. This gives you:
P/T = nR/V
Let's say you fill your tank at 70 deg F which results in a pressure of 4500 psi. But then you move it to a hot car that causes the tank to reach 120 deg F (not unheard of in a hot car). Since nR/V (the right side of the equation above) is constant, you can say P1/T1 = P2/T2. You know P1, T1, and T2 so now you can solve for P2.
P1/T1 = P2/T2
4500/70=P2/120
P2=120*(4500/70)
P2=7714.3 psi
So by leaving your 4500 psi cylinder filled at 70 deg F in a hot car and allowing the cylinder to reach 120 deg, the pressure will reach a little over 7700 psi!! Cars can get even hotter than this, so this is definitely something to think about!
And yes, filling your tank initially at a hotter temperature while cause the pressure to not rise as much.
This is a good question to ask yourself if you ever have plans of packing up your gun and cylinder in the vehicle with plans to go to work all day and then go to the range afterwards. How hot is your cylinder and gun going to while you're at work?
-Clayton
Note: in the P1/T1=P2/T2 equation it is ok to use whatever pressure or temperature units you want since you are using the the same on both sides. The ideal gas law (PV=nRT) technically requires P to be in Pascals, V in cubic meters, and T in Kelvin when using the SI unit version of R=8.314 Pa⋅m3/(K⋅mol).
