Problem $3.$ We plan to liquify propane with the Linde process shown below. In brief, we compress a mixture of feed and recycle streams $(1$ and $9)$ to $80.$ bar, cool it to $480K,$ pass it through a heat exchanger for additional cooling, and throttle it to $1$ bar. This process results in a vapor$-$liquid mixture. We collect the liquid fraction, and we pass the vapor fraction through the heat exchanger, which heats it to $470K.$

a$.$ What fraction of the mixed feed $($i$.$e$.,$ stream $2)$ is liquified in the process?

b$.$ Show the process on a P$-$H diagram that is on the next page.