$($a$)$ Nitrogen gas enters a compressor at $100$ kPa and $300$ K $,$ and exits at $800$ kPa and $450$ K $.$ An amount of at $40k\frac{J}{k}g$ of heat is lost to the surroundings. Assuming constant specific heat at $300$ K $,$ answer the following questions.

$($i$)$ Determine the work required by the compressor $($in $k\frac{J}{k}g).$

$($ii$)$ Calculate the entropy change of nitrogen $($in $k\frac{J}{k}g*K).$

$[4$ marks$]$

$[3$ marks$]$

$($b$)$ Steam flows through an adiabatic nozzle, entering at $1$ MPa and $300C$ with a velocity of $50\frac{m}{s}.$ The nozzle is designed to exhaust steam at $0\mathrm{.}2$ MPa and $200C.$

$($i$)$ Determine the velocity of the steam at the nozzle exit $($in $\frac{m}{s}).$

$[5$ marks$]$

$($ii$)$ Determine the maximum possible velocity of the steam at the nozzle exit $($in $\frac{m}{s}).$

$[5$ marks$]$

$($iii$)$ Sketch the process in $($ii$)$ above on a $T-s$ diagram.

$[3$ marks$]$