We are interested in measuring CH$4$ sorption in a polymer using a constant volume$-$variable

pressure device. The experimental apparatus is formed by two volumes, Va $=30$ cm$3$ and Vb $=$

$25$ cm$3,$ separated by a valve and submerged in a liquid bath to keep temperature constant at

$35\backslash$deg C$.$ The system is$,$ at the beginnings, under vacuum and $0\mathrm{.}5$ g of polymer are enclosed in the

volume Vb$.$ The valve V is closed and CH$4$ is fed to the volume Va until reaching a pressure of

$100$ psi. The valve V is then opened $($for a few seconds$)$ and closed, to allow gas to flow into the

volume Vb$.$

$1.$ Calculate the pressure in both compartments after gas expansion.