$5-13.$ A steady$-$state liquefaction process generates $100l\frac{b_m}{m}in$ of saturated liquid methane at $P=10$ psia. Fresh methane enters the process at $T=75F$ and $P=10a,$ and is mixed with the recycled methane to form the "methane feed" stream. This enters a heat exchanger $($HX$1)$ that cools the methane feed to $T=-100F$ and $P=10$ psia. The process has two compressors $($both $=0\mathrm{.}75$ : the first compresses the methane to $P=100$ psia and the second compresses the methane to $P=1000$ psia$).$ Each compressor is followed by a heat exchanger $($HX$2$ and HX$3)$ that cools the methane to $T=-100F$ without changing the pressure. Next, the supercritical methane enters a counter$-$current heat exchanger $($HX$4)$ in which the methane vapor from the flash chamber is used as the coolant. The coolant leaves HX$4$ at $T=-110F$ and is recycled into the "methane feed" stream. The supercritical methane leaves HX$4$ and enters a flash chamber, where its pressure is reduced to $P=10$ psia.

A$.$ Determine the flow rate of the supercritical methane entering the flash chamber.

B$.$ Determine $W$ for each of the two compressors.

C$.$ Determine $Q$ for each of the four heat exchangers.