a$)$ A $10$ TR system using R$-12$ is operate on a two stage vapour compression refrigeration system with a flash chamber. The refrigerant is evaporating at $-15C,$ flash chamber works on an intermediate temperature of $10C,$ and condensation takes place at $40C.$ Low pressure compressor and expansion valve operate between $-15C$ and $10C$ and the high pressure compressor and expansion valve operate between $10C$ and $40C.$ Saturate vapour enters both the compressors and saturated liquid enters each expansion valve. Sketch system $($flow diagram$)$ and the p$-$h diagram giving relevant property values. Find $($i$)$ Mass flow rate of refrigerant through LP and HP compressor., $($ii$)$ COP of the system.