A power plant uses heat from a nuclear reaction to produce work. Water flows through a pump, boiler, turbine, condenser, and back to the pump in a continuous cycle. The boiler pressure is $5\,\text{MPa}$ and the condenser pressure is $10\,\text{kPa}$. The pump and turbine have isentropic efficiencies of ${0.735}$ and ${0.805}$ respectively. The turbine inlet temperature is $400\,^\circ\text{C}$, and the condenser outlet is saturated liquid. What are

1. The quality at the turbine outlet
2. The temperature rise across the pump due to irreversibilities
3. The work input to the pump, per kg of steam
4. The heat input to the boiler, per kg of steam
5. The work output from the turbine, per kg of steam
6. The heat rejection from the condenser, per kg of steam
7. The thermal efficiency
8. The lowest possible temperature of the thermal reservoir that this heat engine accepts heat from
9. The highest possible temperature of the thermal reservoir that this heat engine rejects heat to
10. The maximum possible thermal efficiency for a device operating between reservoirs at the above temperatures

Note: This question will take a long time, and has been assigned a very high weight to account for this fact. It may be more convenient to calculate these results in a different order Answers:

1. $x_\text{turb out} =$ (answer tolerance: $0.01$)
2. $\Delta T_\text{pump} =$ $^\circ\text{C}$ (answer tolerance: $0.01\,^\circ\text{C}$)
3. $w_\text{pump in} =$ $\text{kJ}/\text{kg}$ (answer tolerance: $0.05\,\text{kJ}/\text{kg}$)
4. $q_\text{boil in} =$ $\text{kJ}/\text{kg}$ (answer tolerance: $1\,\text{kJ}/\text{kg}$)
5. $w_\text{turb out} =$ $\text{kJ}/\text{kg}$ (answer tolerance: $1\,\text{kJ}/\text{kg}$)
6. $q_\text{condenser out} =$ $\text{kJ}/\text{kg}$ (answer tolerance: $1\,\text{kJ}/\text{kg}$)
7. $\eta =$ (answer tolerance: $0.05$)
8. $T_\text{hi} =$ (answer tolerance: $0.01\,^\circ\text{C}$)
9. $T_\text{lo} =$ (answer tolerance: $0.01\,^\circ\text{C}$)
10. $\eta_\text{max} =$ (answer tolerance: $0.05$)