$9\mathrm{.}3$ A two$-$stage reciprocating compressor compresses propane from $1$ to $235$ psig $(7$ kPa to $16\mathrm{.}2$ barg$)$ in a refrigeration system. The compression ratio is the same in both stages. Suction temperatures to the first and second stages are $-20F(-28\mathrm{.}9C)$ and $80F(26\mathrm{.}7C).$ The adiabatic compressor efficiency is $80\%.$

a$.$ Compute the isentropic work required $(Bt\frac{u}{l}{b}_m,k\frac{J}{k}g)$ in each stage of the propane compressor and the discharge temperature assuming ideal gas behavior.

b$.$ Compute the isentropic work required $(Bt\frac{u}{l}{b}_m,k\frac{J}{k}g)$ in each stage of the propane compressor and the discharge temperature using the PH diagrams in Appendix B$.$