$5.(20$ points$)$ Air enters a compressor operating at steady state at $\backslash (45^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $3$ bar with a volumetric flow rate of $\backslash (1\mathrm{.}5\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$min$\}\backslash )$ and is compressed isothermally to $20$ bar. There are no irreversibilities within the compressor. Employing the ideal gas model and ignoring kinetic and potential energy effects, obtain the following results:

a$.$ For a control volume enclosing the compressor only, determine the heat transfer rate and the power input.

b$.$ Calculate the rate of entropy production for an enlarged control volume enclosing the compressor and a portion of its immediate surroundings where the heat transfer occurs at the ambient temperature, $\backslash (17^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Explain why the entropy production value differs from what was used to solve part $($a$)$