Rankine Cycle

Ideal steam power cycle — working fluid undergoes phase change. Water is pumped as a liquid, heated and evaporated in a boiler, expanded through a turbine, and condensed back to liquid. The H–S (Mollier) diagram is the primary design tool. Condenser fixed at P_c = 10 kPa. Steam table data from IAPWS-IF97.

Boiler pressure P_b4.0 MPa

Superheat ΔT_sh100 °C

Performance

Cycle efficiency

34.4%

Carnot (same T limits)

48.8%

Turbine work W_T

972 kJ/kg

Pump work W_P

4.0 kJ/kg

Back-work ratio

0.41%

Turbine exit quality

x₄ = 0.772(erosion risk)

Cycle Diagrams

1→2 Isentropic pump (liquid)

2→3 Isobaric heat addition (boiler)

3→4 Isentropic expansion (turbine)

4→1 Isobaric heat rejection (condenser)

Dashed curve = saturation dome (boundary between liquid, wet steam, and superheated vapor regions). On the H–S diagram, the vertical drop 3→4 equals turbine work output W_T. Evaporation (2→3 across dome) is a straight line on H–S — a key Mollier diagram property.

State Properties

State	Description	T (°C)	P (MPa)	h (kJ/kg)	s (kJ/kg·K)	v (m³/kg)
1	Sat. liquid	45.8	0.010	191.8	0.6493	0.00100
2	Compressed liquid	45.8	4.000	195.8	0.6493	0.00100
3	Superheated steam	350.4	4.000	3010.4	6.4367	0.0719
4	Wet steam x = 0.772	45.8	0.010	2038.1	6.4367	11.3190

Key Relations

Thermal efficiency

η = (W_T − W_P) / Q_in = 1 − Q_out/Q_in

Pump work (liquid, incompressible)

W_P = v_f · (P_b − P_c) [kJ/kg]

Turbine exit quality

x₄ = (s₃ − s_f) / s_fg (want x > 0.85)

Back-work ratio (very small vs Brayton)

BWR = W_P / W_T ≈ 0.5–2%