$[1]$ A well$-$insulated rigid container is separated into two subsystems by a piston $($see the figure$)$ that

is held in place by stops. The first subsystem $($A$)$ is filled with an ideal gas at $2$ bar $,$ and the second

subsystem $($B$)$ is filled with the same ideal gas at a pressure of $1$ bar $.$ The piston is diathermal, and

the initial temperature in both subsystems is $300$ K and the length of the initial volume of gas on each

side is $10c{m}^3.$ The cross$-$sectional area is the same on both sides of the partition. The piston is

slightly lubricated, but considerable friction is still present. At some time, $t=0,$ the stops are removed.

After all of the oscillations have ceased and the system is at rest, the pressures in both subsystems

are identical. Assuming that the gases have a constant $Cv=12\mathrm{.}6\frac{J}{m}$olK, what are the final

temperatures?

$[2]$ Consider the same situation as problem $[1]$ but with the piston now being adiabatic. What are the

final temperatures after the pressures have equalized.$[1]$ A well$-$insulated rigid container is separated into two subsystems by a piston $($see the figure$)$ that

is held in place by stops. The first subsystem $($A$)$ is filled with an ideal gas at $2$ bar $,$ and the second

subsystem $($B$)$ is filled with the same ideal gas at a pressure of $1$ bar $.$ The piston is diathermal, and

the initial temperature in both subsystems is $300$ K and the length of the initial volume of gas on each

side is $10c{m}^3.$ The cross$-$sectional area is the same on both sides of the partition. The piston is

slightly lubricated, but considerable friction is still present. At some time, $t=0,$ the stops are removed.

After all of the oscillations have ceased and the system is at rest, the pressures in both subsystems

are identical. Assuming that the gases have a constant $Cv=12\mathrm{.}6\frac{J}{m}$olK, what are the final

temperatures?

$[2]$ Consider the same situation as problem $[1]$ but with the piston now being adiabatic. What are the

final temperatures after the pressures have equalized.