It seems that a solution to the following problem is strangely absent from the internet. After days of research, I have found no one who offers such a solution. Only one paper addressed it but was sloppy in the way it presented the equations; they were incomplete. The problem is simply this...Given a pressurized tank with a given mass of REAL gas within, at an initial pressure and temperature, what will the internal temperature be at any time (t) when (n) moles/sec of additional gas is added at a given inlet temperature? This looks like a squirly differential problem and numerical solution, and I am trying to incorporate the Van der Waals equation of state, NOT the ideal gas equation. If I have the initial tank pressure at say, 4000psi @ 100 degF temperature, and I add (n) moles / sec at 34 degF, I would expect the tank temperature to drop as the cold inlet gas immediately begins colliding with the molecules already in the tank and before the energy in the tank gets thoroughly mixed. But then, due to more collisions per second overall and therefore higher pressure, I would expect that there would also be a heating effect that predominates (I know that whenever you add gas to a tank, that it heats up). So what portion of the input energy converts to the average internal pressure, and how much to the average internal temperature? In researching for a solution to this tank filling problem, I figured I would probably be looking at some differential equations for real gases dealing with adding mass and therefore energy to the tank. But I ended up with references along the lines of U = f (T). How can I know what the internal energy change is in the tank if it requires me to know temperature change first?! And if I work backwards, how can I know what the temperature change is if it requires me to know the internal energy change first?! I do not know either.