Question No$\mathrm{.}16$: In a boot$-$strap refrigeration system for an aircraft the ambient conditions are $0\mathrm{.}225$ bar and $-50C.$ Cooling load estimate is $20$ ton refrigeration $(20TR.$ The speed of the plane is $1000k\frac{m}{h}r.$ Ram efficiency is $0\mathrm{.}9.$ the pressure ratio for the main compressor is $3\mathrm{.}5$ and this bled off air is further compressed in secondary compressor run by cooling air turbine on a single shaft such that output from turbine is equal to input to the compressor. The internal efficiency of main compressor as well as secondary compressor is $0\mathrm{.}9,$ and that of cooling turbine is $0\mathrm{.}8.$ The air from secondary compressor is cooled by ram air to $50C.$ The cooling air turbine running the secondary compressor has its exit pressure of $1$ bar. Determine $($i$)$ Delivery pressure from the secondary compressor, $($ii$)$ Mass flow rate bled for cooling the cabin, $($iii$)$ COP of the system.