$($a$)$ A chemical plant steam turbine uses steam at $1368$kPa and $372C.$ The steam is discharged at $137000Pa.$ The turbine operates adiabatically and the feed and discharge velocities are found to be equal. Calculate the work done by the turbine when it uses $1650kg$ of steam per hour. Given: Enthalpy of superheated steam at $1368$kPa and $372C$ is $3200k\frac{J}{K}g$ and Enthalpy of saturated steam at $1368$kPa and $372C$ is $2690k\frac{J}{K}g.$

$[8$ marks$]$

$($b$)$ In a single stage compressor, $20kg$ of air is compressed from $1$ bar, $300K$ to $5$ bar. This process obeys the equation $P{V}^{1\mathrm{.}25}=$ constant. Molar mass of air is $29\mathrm{.}0\frac{g}{m}ol.$

Determine the work done and heat involved in this process.

Given:For air $C_P=27\mathrm{.}458+6\mathrm{.}1839{10}^{-3}T-8\mathrm{.}9932{10}^{-7}{T}^2\frac{kJ}{\text{k}\text{m}\text{o}\text{l}\text{.}K}.$

$[20$ marks$]$