The design specifications for a steady$-$state, work$-$producing device call for it to receive heat at a rate $Q^{}$ from a heat source and deliver work at the rate $W^{}.$ The device will operate reversibly and isothermally at $500C.$ A single stream of ideal gas at $500C$ and $20$MPa enters the device, and two streams of ideal gas at $500C$ and pressures of $3\mathrm{.}0$MPa and $0\mathrm{.}1$MPa leave the device. Each stream leaving has half the molar flow rate of the feed stream. Determine the work done per mole of fluid fed to the device. $($ANS: $-23$ kJ$/$mol$)$