Rankine Cycle Thermal Efficiency

William Rankine set out the steam cycle in the 1850s and the arithmetic has not changed: net work over heat in, with every term read off a steam table. Take 3 MPa and 350 °C into the turbine against a 10 kPa condenser. The turbine drops the steam from 3116 to 2136 kJ/kg, the feed pump lifts the condensate by about 3 kJ/kg, and the boiler puts back 2921. That is $(979.9 - 3.0)/2921 = 33.4\%$, and a real 1950s station would have measured something close.

The pump work is the term everybody wants to drop, and for a first pass they are right. Compressing a liquid costs $v\,\Delta P$, which for water lifted from 10 kPa to 3 MPa is about 3 kJ/kg against a turbine output near 980, so it is 0.3% of the gross. This is the whole reason the Rankine cycle uses a condenser at all rather than running a gas back through a compressor: the Brayton cycle spends half its turbine output driving its own compressor, and the Rankine cycle spends three parts in a thousand. Condensing the working fluid before pressurising it is the single best trick in power engineering.

What is genuinely counterintuitive is where the efficiency gains come from. Lowering the condenser pressure buys more than raising the boiler pressure, because it stretches the temperature range at the cheap end, and this is why a coastal plant with cold seawater beats an inland one on identical hardware. It is also why a station's efficiency drops measurably in August. The limit is that a lower condenser pressure means wetter steam at the turbine exhaust, and below about 88% dryness the water droplets erode the last-stage blades, which is what reheat stages exist to prevent.