Problem #$2$: $(50$ pts$.)$

Two kilograms of an ideal gas with constant $cp=1\frac{k}{\frac{?}{?}}kgK$ and $cv=0\mathrm{.}7\frac{k}{\frac{?}{?}}kgK$ are contained in an insulated piston$-$cylinder device with an initial volume of $0\mathrm{.}3m^{\text{'}}$ and a pressure of $10$ bar $.$ The piston is then allowed to move until the volume quadruples.

If the process is considered reversible, determine:

a$)$ The temperature of the final state in $K.$

b$)$ The work in $\frac{k}{?}.$

If irreversibilities during the process cause the entropy to increase by $0\mathrm{.}1k\frac{J}{K},$ determine:

c$)$ The temperature of the final state in $K.$

d$)$ The work in K $.$

Complete the following for the given problem $($encompassing both reversible and irreversible processes$)$

e$)$ Define the correct engineering model

f$)$ Draw an engineering diagram $($neat schematic$)$

g$)$ Sketch the reversible and irreversible processes in a T$-$s diagram.

Instruction: Begin your response in the space provided below. If additional space is required, you may attach extra sheets to your submission. Please ensure that all attachments are properly labeled. Ensure that you provide detailed step$-$by$-$step calculations for each part of the problem.