A $100$ TR system using $R-12$ is operate on a two stage vapour compression refrigeration system with a flash chamber. The refrigeraunt is evaporating at $-40C,$ flash chamber works on an intermediate tempenture of $0C,$ and condensation takes place at $30C.$ Low pressure compressor und expunsion valve operate between $-40C$ and $0C$ and the high pressure compressor and expansion valve operate between $0C$ and $30C.$ Sarurate vapour enters both the compressors and saturnted liquid enters each expansion valve. Sketch system $($fow diagram$)$ and the p$-$t diayram giving relovant property values. Find $($i$)$ Mass flow rate of refrigerant through LP and HP compressor., $($ii$)$ COP of the system.