$4.(30$ points$)$ A piston$-$cylinder device contains $5$ kg of refrigerant$-134$a at $600$ kPa and $\backslash (70^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The refrigerant undergoes various processes, and you need to analyze the state of the substance and perform energy calculations.

a: State Determination $(10$ points$)$

Using thermodynamic tables, determine the specific volume of the refrigerant$-134$a at the initial state $\backslash (\backslash$left$(600\backslash$mathrm$\{$kPa$\}\backslash$right$.\backslash )$ and $\backslash (\backslash$left$\mathrm{.}70^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash$right$)\backslash ).$

Identify whether the refrigerant is in a compressed liquid, saturated mixture, or superheated vapor state at this condition. Justify your answer using the properties from the tables.

b: Phase Change Process $(10$ points$)$

If the refrigerant is cooled at constant pressure until it reaches a saturated liquid state, determine the temperature and specific volume at this final state.

How much heat is removed from the refrigerant during this process? c: Isothermal Expansion$($iv puinis$)$

Now, assume the refrigerant expands isothermally from its initial state at $\backslash (70^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ until the pressure drops to $300$ kPa $.$ Determine the final state and specific volume of the refrigerant at the end of this process.

Calculate the work done during this isothermal expansion process, assuming the refrigerant behaves as an ideal gas.