Mu$$strame c$$mo resolver: A two$-$stage, double$-$acting compressor draws in $0\mathrm{.}038$ kg$/$s of air at $27$C and $0\mathrm{.}07$ bar. The low$-$pressure compressor discharges at $0\mathrm{.}35$ bar and the pressure drop between stages is $0\mathrm{.}07$ bar. The high$-$pressure compressor receives water from an intermediate cooler at $32$C and discharges it at $1\mathrm{.}4$ bar. Compression is polytropic with n $=1\mathrm{.}5$ and the dead space is $5\%$ in each cylinder. Air will be used.

a$)$ Determine the quantity of water that must circulate through the intermediate cooler if its temperature rise is $6$C$.$

b$)$ Determine the power of each compressor.

c$)$ Determine the size of the low$-$pressure cylinder for a speed of $300$ rpm and L$/$D $=1\mathrm{.}25.$