Calculating residual pressure in storage tanks after cylinder action

in the 2007CON_Pneumatic_Power_Olivera.pdf presentation, Raul Olivera gives an example of a reservoir cylinder system where he says that after 2 pushes and one pull the reservoir pressure has dropped to less than 20 psig, after having started at 120 psig.
It would be helpful if he had included some information on how the calculation was done. Perhaps something on conservation of mass or energy.

Lots of ways to do it… a good starting point is to use PV=nRT. Start with the known tank P and V. Equalize to the Vtank + Vcylinder state, constant nRT; P goes down. Remove cylinder volume; new “n”. Rinse and repeat.

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