The Rankine cycle is the working principle behind virtually every steam and coal power plant. Water circulates through four steady-flow devices, using its own phase change (liquid ⇌ vapor) to carry energy. The top panel shows the physical flow loop; the bottom panel is the same cycle drawn on a temperature–entropy (T–s) diagram — the standard way engineers read a heat engine's performance at a glance.
1→2 Boiler: constant-P heat addition, liquid → saturated vapor
2→3 Turbine: near-isentropic expansion, vapor drives a shaft
3→4 Condenser: constant-P heat rejection, vapor → saturated liquid
4→1 Pump: near-isentropic compression back to boiler pressure
State 1 leaves the boiler as saturated vapor at Phigh (enthalpy h₁, entropy s₁ from steam-table saturation data). Turbine expansion to Plow is modelled with an isentropic ideal (s₂s = s₁, giving vapor quality x₂s) corrected by the isentropic efficiency ηt — this is exactly why the real state 2 sits to the right of the dashed ideal state 2s on the T–s diagram, the entropy increase is the irreversibility:
x₂s = (s₁ − s_f,low) / (s_g,low − s_f,low)
h₂s = h_f,low + x₂s·(h_g,low − h_f,low)
h₂ = h₁ − η_t·(h₁ − h₂s)
x₂ = (h₂ − h_f,low) / (h_g,low − h_f,low)
The condenser drops the fluid to saturated liquid (h₃ = h_f,low) at constant temperature — a horizontal line on the T–s diagram. The pump then raises its pressure back to Phigh; because liquid is nearly incompressible this costs very little work and barely moves the state point:
w_pump = v_f·(P_high − P_low) (kJ/kg, P in kPa)
h₄ = h₃ + w_pump
W_net = (h₁ − h₂) − w_pump
Q_in = h₁ − h₄
η = W_net / Q_in
- Boiler pressure — raising it pushes the whole cycle toward higher average heat-addition temperature, which is the main lever for real power-plant efficiency (the "high-pressure superheat" that modern boilers chase). On the T–s diagram the whole loop shifts upward.
- Condenser pressure — dropping it (running the condenser under vacuum, cooled by a river or cooling tower) widens the turbine's pressure drop and is the second big efficiency lever; the loop stretches downward and sideways.
- Turbine efficiency — real turbines are not perfectly isentropic; friction and flow losses turn some of the ideal work into extra exhaust enthalpy instead — the gap between state 2 and the dashed ideal state 2s.
- Turbine exit quality x₂ — real turbines are kept above roughly 88–90% quality; wetter steam erodes the last-stage blades, which is why plants reheat steam mid-expansion in practice.
Saturation properties (Tsat, hf, hg, sf, sg) are interpolated from standard steam-table data points spanning 0.05–220.9 bar (the critical point) and drawn as the shaded two-phase dome on the T–s diagram. The liquid preheat leg (state 4 → saturation) uses the standard incompressible-liquid approximation ds ≈ cp·dT/T with cp ≈ 4.18 kJ/kg·K, since compressed-liquid entropy isn't part of the saturation table.