# Thermodynamics of gas exchange between gas cylinders

A synthesis gas mixture ($\text{H}_2:\text{CO}$ with molar proportion 2:1) is needed for methanol synthesis. The final mixture must be available in a gas cylinder of 50 L, say cylinder $M$, which contains, initially, pure $\text{H}_2$ at 5 bar. The carbon monoxide which will compose the final mixture is available in a smaller cylinder (20 L), say cylinder $m$ in a volumetric proportion of 9:1, at 120 bar. Both cylinders are, initially, at 303 K. A 1/8” steel tube must be used with a globe valve placed 1 m from the small cylinder $m$ and 4 m from the cylinder $M$.

How can one calculate the pressure and temperature of both cylinders in the process where the gas transfer is done opening totally and suddenly the globe valve, after 15 s? The dynamics of the problem seem to be difficult to implement.

• This seems like a homework question. What have you tried? A globe valve doesn't suddenly open. It takes quite a few rotations of the handle to fully separate the plug from the seat. Assuming you have a valve that can be suddenly opened fully, try assuming that your final temp and pressure equalize, then figure out the volume of each species now in each cylinder. – morristtu May 2 '16 at 8:49