i$)$ A piston $($A$)$ and piston rod $($B$)$ are fitted inside a

cylinder of length $0\mathrm{.}51$ m and area $6\mathrm{.}4{10}^{-3}{m}^2($see

diagram$).$ Although the piston is quite thin, it

weighs $9\mathrm{.}05$ kg ; the piston rod is $1\mathrm{.}29{10}^{-3}{m}^2$ in

area and weighs $4\mathrm{.}50$ kg $.$ On top of the rod, but

outside the cylinder, an $18\mathrm{.}10$ kg weight $($C$)$ is

placed. Originally, gas in D is at atmospheric

pressure while the piston is positioned in the middle

of the cylinder. Gases D and E are helium and under

these conditions may be considered ideal with a

constant $Cv=12\mathrm{.}6\frac{J}{?}$ gmmol K$.$ The initial temperature everywhere is $321$ K $.$ Assume that

the cylinder is insulated and the piston is a good conductor. Also assume that the cylinder,

piston, and piston rod have negligible heat capacity. If weight $C$ should fall off, what is the

final state of the system when the piston has stopped and there is a balance of forces across

the piston? Do not neglect the fact that during motion there may be some friction between

moving parts.