Problem $4$:

Steam was measured to be entering the turbine of a small Rankine cycle$-$based power plant at a pressure of $225$ psia. The temperature of this steam was $\backslash (590^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$ at the entrance of the turbine and was measured at the exit with a temperature and pressure of $\backslash (405^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$ and $140$ psia, respectively. Over the course of $10$ minutes, a total of $1910$ mL of water passed through the turbine. The rate of fuel being added to the boiler of the system was $1\mathrm{.}1$ gallons$/$minute$.$ The electric generator attached to the system was outputting $299$ Watts during the measurement interval. The LHV of the fuel being used was validated to be $\backslash (2520\backslash$mathrm$\{$Btu$\}/\backslash$mathrm$\{$ft$\}^\{3\}\backslash ).$ Calculate the mass flow rate of steam being produced by the boiler in $\backslash (\backslash$mathrm$\{$lbm$\}/\backslash$mathrm$\{$hr$\}\backslash ),$ the rate of work output from the turbine in Btu$/$hr$,$ the rate of energy input to the boiler from the fuel in Btu$/$hr$,$ and the system's total efficiency.