An air craft moving with speed of $1000$ km$/$h uses simple gas refrigeration cycle for air conditioning. The ambient pressure and temperature are $0\mathrm{.}35$ bar and $-10\backslash$deg C respectively. The pressure ratio of compressor is $4\mathrm{.}5.$ The heat exchanger effectiveness is $0\mathrm{.}95.$ The isentropic efficiencies of compressor and expander are $0\mathrm{.}8$ each. The cabin pressure and temperature are $1\mathrm{.}06$ bar and $25\backslash$deg C$.$ Determine temperature and pressures at all points of the cycle. Also find the volume flow rate through compressor inlet and expander outlet for $100$ TR$.$ Take CP$=1\mathrm{.}005$ kJ$/$kg K; R$=0\mathrm{.}287$ kJ$/$kg K and CP$/$CV$=1\mathrm{.}4$ for air.