Methane is liquefied in a Claude liquefaction system as shown below. Gaseous Methane is compressed to $80$ bar and precooled to $300$ K $($stream $4).$ This high$-$pressure methane gas is further cooled in heat exchanger I to a temperature of $260$ K $($steam $5)$ and then split into two streams, a draw$-$off stream of $15\%$ to the expander $($stream $11)$ with the main stream $($the remaining $85\%)$ flowing to the throttle valve via heat exchanger II $($streams $6$ to $7).$ The expander and throttle valve exhaust to a pressure of $1$ bar $($streams $12$ and $8).$ The temperature of the methane gas leaving the expander $($stream $12)$ is $150$K$.$ Recycle methane gas $($stream $15)$ leaves the exchanger system at $1$ bar and $280$ K$.$Determine the following:i$)$ The specific enthalpy $($kJ$/$kg$)$ of streams $4,11,12$ and $15$ii$)$ If $100$ kg$/$h of liquid methane $($stream $9)$ is produced, the required mass flow rate $($kg$/$h$)$ of methane in streams $4,8,10,11$ and $15.$iii$)$ The temperature $(\backslash$deg C$)$ and specific enthalpy of streams $7,8,13$ and $14.$iv$)$ The power $($kW$)$ generated by the expander and the efficiency of the expanderNote: You may assume that there is no pressure drop across the heat exchangers or the separator for this process.Properties of saturated methane at $1$ bar: Temperature $=111$ K Specific enthalpy of liquid, Hf $=285\mathrm{.}4$ kJ kg$-1$ Specific enthalpy of vapour, Hg $=796\mathrm{.}9$ kJ kg$-1$ Specific entropy of liquid, Sf $=4\mathrm{.}928$ kJ kg$-1$ K$-1$ Specific entropy of vapour, Sg $=9\mathrm{.}521$ kJ kg$-1$ K$-1$