Hi to all of you enthusiasts,
I have a 1 liter compressed air tank with around 207 bar of air pressure inside. It has been sitting out for a while and I am assuming its temperature has almost reached the surrounding temperature which is 40 degrees Celsius. I am also assuming that the surrounding is at around 1 bar (atmospheric pressure). I am not sure how to go about calculating the air temperature as it leaks out of the tank so I can predict any potential frosting.
I did use the ideal gas law of $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$ where $P_1$, $V_1$ and $T_1$ belong to the tank and $P_2$, $V_2$ and $T_2$ belong to the surrounding. I thought if any volume of air leaks to the surrounding its volume would increase by 207 times (i.e. $207\times V_1 = V_2$), because the tank can contain 207 times more air than the atmosphere (which has roughly 1 bar of pressure). However, the resulting temperature ends up being 40 degrees Celsius again. Am I doing this right? Any help or hint is appreciated.