Problem $3$ A rigid insulated container has two rooms separated by a membrane. Room A contains $1$ kg air at $200C$ and room B has $1\mathrm{.}5$ kg air at $20C,$ both rooms at $100$ kPa $.$ Consider two different processes, set each process up as a separate solution.

$3\mathrm{.}1)$ Heat transfer between A and $B$ creates a final uniform $T.$

$3\mathrm{.}2)$ The membrane breaks and the air comes to a uniform state.

For both processes:

a$)$ find the final temperature,

b$)$ find the final pressure$($s$)$

c$)$ find the entropy generation.

d$)$ Case $1$ has less entropy generated and hence more potential to do work. How is the final state for case $1$ able to potentially do more work than the final state of case $2?$

e$)$ For each case draw the process on a Pv diagram and on a Ts diagram. Use a separate graph for each case.

You must use specific heat capacities and the ideal gas law for this problem, not tables.