$($a$)$ Air with $0\mathrm{.}2m^3$ volume at $4$ bar and $130C$ is contained in a system. A reversible

adiabatic expansion takes place till the pressure falls to $1\mathrm{.}02$ bar $.$ The gas is then

heated at constant pressure till enthalpy increases by $72\mathrm{.}5$ kJ $.$ Given the mass of air is

$0\mathrm{.}694$ kg $,$ Calculate the work done: Take $R=0\mathrm{.}287K\frac{J}{K}gK$

$[12$ marks$]$

$($b$)$ Air is compressed by an adiabatic compressor with an isentropic efficiency of $95\%$

from $100$ kPa and $20C$ to $700$ kPa $.$ Assuming variable specific heats and neglecting

the changes in kinetic and potential energies, determine the power input to the

compressor.