Problem 1 (20 points): Consider the open thermodynamic system shown in the diagram below. The system, whose components are unknown, operates in steady state with water as its working fluid. The following operating conditions are known:
$m_2 = 7.50$ kg/s, $m_4 = 9.20$ kg/s, $Q_1 = 12.6$ MW, $Q_2 = 25.0$ MW, $W_1 = 5000$ kW, $W_2 = 9400$ kW
Determine the two unknown flow rates, $m_1$, and $m_3$.
$P_3 = 100$ kPa
$x_3 = 0.75$
$P_1 = 250$ kPa
$T_1 = 80$ °C
$P_2 = 10$ kPa
$T_2 = 40$ °C
$P_4 = 1200$ kPa
$T_4 = 350$ °C