Problem $2(4$ points total$)$

We have a $2m^3$ tank initially filled with an ideal gas at $0\mathrm{.}1$MPa and $300K.$ Our goal is to pressurize

this vessel to $1$MPa, using a large external source of an ideal gas maintained at $300$ bar and $300$

$K.$ The gas has a constant pressure heat capacity tilde$(C{)}_p=20\mathrm{.}9\frac{J}{\text{m}\text{o}\text{l}\text{K}}.$

In our model, we assume that the initial gas in the vessel $($layer A$)$ doesn't mix with the incoming

gas $($layer B$).$ Layer A is compressed by the entering gas $($layer B$)$ from $0\mathrm{.}1$ to $1$MPa. As a result,

the final system contains two layers of gas, both at $1$MPa but potentially at different temperatures.

Assumptions:

There's no heat transfer between the gas layers.

There's no heat transfer to the vessel during the process.

A$.$ Calculate the final temperatures in layers A and $B.$

B$.$ Calculate the entropy generated by the gas inside the vessel during the pressurization process

C$.$ If we thermally isolate the system $($layers A and B$)$ from the environment and do not allow any

additional gas to enter, what is the maximum work we can obtain through reversible mixing of $A$

and $B$ within the same vessel to reach a final homogeneous temperature? What will be the final

temperature and pressure in this case?