A turbine in a steam power plant exhausts directly to the atmosphere at $P = 100\,\text{kPa}$. The working fluid leaves as a saturated vapour with $x = {0.878}$. The chief engineer suggests that it might be possible to improve upon this by installing a condenser after the turbine. In the engineer’s plan, the condenser would change the outlet state of the turbine to a saturated mixture at $P = 50\,\text{kPa}$ with quality $x = {0.850358}$.

1. How much extra work would be extracted from the turbine, per kilogram of steam processed, if the outlet state were changed as described above?
2. In order to maintain the partial vacuum in the condenser, a pump would need to be fitted to its outlet. The pump would accept saturated liquid water at $P = 50\,\text{kPa}$ and reject compressed liquid water at the same temperature but at atmospheric pressure $P = 100\,\text{kPa}$. If the pump were to operate adiabatically, how much energy would be required to power the pump, per kilogram of water processed? (Note: your answer should require only one table look-up)
3. Considering the pump and the turbine together, what is the net change in the plant’s power output (per kilogram of stream) associated with installing the condenser?

You may neglect changes in kinetic and potential energy in all parts of this problem Answers:

1. $w_\text{gain} =$ $\text{kJ/kg}$
2. $w_\text{pump} =$ $\text{kJ/kg}$
3. $w_\text{net} =$ $\text{kJ/kg}$