The Rankine steam cycle is the basic model for many power plants that use water and steam to turn heat into mechanical work. This cheat sheet helps students track the four main devices: pump, boiler, turbine, and condenser. It is useful because Rankine problems often require careful use of enthalpy, entropy, pressure, temperature, and steam tables.
A clear reference reduces confusion between the ideal cycle and real component behavior.
In the ideal Rankine cycle, the pump and turbine are isentropic, the boiler adds heat at high pressure, and the condenser rejects heat at low pressure. The main formulas compare turbine work, pump work, heat added, heat rejected, and thermal efficiency. Steam quality describes the fraction of a saturated mixture that is vapor.
Real cycles include losses, so isentropic efficiency is used to compare actual devices with ideal ones.
Key Facts
- The ideal Rankine cycle has four processes: 1 to 2 isentropic pump compression, 2 to 3 constant-pressure heat addition, 3 to 4 isentropic turbine expansion, and 4 to 1 constant-pressure heat rejection.
- Pump work for an incompressible liquid is approximately w_p = v_f(P2 - P1), where v_f is saturated liquid specific volume.
- Turbine work is w_t = h3 - h4 for a steady-flow turbine with negligible kinetic and potential energy changes.
- Boiler heat input is q_in = h3 - h2, where h3 is the turbine inlet enthalpy and h2 is the pump outlet enthalpy.
- Condenser heat rejection is q_out = h4 - h1, where h4 is the turbine outlet enthalpy and h1 is the condenser outlet enthalpy.
- Net work output is w_net = w_t - w_p, and thermal efficiency is eta_th = w_net / q_in.
- For a saturated mixture, steam quality is x = (h - h_f) / h_fg, and the mixture enthalpy is h = h_f + xh_fg.
- Turbine isentropic efficiency is eta_t = (h3 - h4_actual) / (h3 - h4s), while pump isentropic efficiency is eta_p = (h2s - h1) / (h2_actual - h1).
Vocabulary
- Rankine cycle
- A thermodynamic power cycle that uses a working fluid, usually water, to convert heat into net work through a pump, boiler, turbine, and condenser.
- Enthalpy
- A property written as h that represents internal energy plus flow energy and is commonly used to calculate heat and work in steam devices.
- Entropy
- A property written as s that helps identify reversible adiabatic processes, where entropy stays constant in the ideal pump and turbine.
- Steam quality
- The mass fraction of vapor in a saturated liquid-vapor mixture, written as x.
- Isentropic efficiency
- A measure of how closely a real turbine or pump matches the ideal constant-entropy process.
- Thermal efficiency
- The fraction of heat input converted into net work, calculated as eta_th = w_net / q_in.
Common Mistakes to Avoid
- Using temperature alone to find steam properties is wrong because pressure or quality is often also needed to identify the state.
- Forgetting pump work is wrong because even though it is small compared with turbine work, it must be subtracted when finding net work.
- Mixing up q_in and q_out is wrong because heat is added in the boiler from state 2 to state 3 and rejected in the condenser from state 4 to state 1.
- Assuming actual turbine expansion is isentropic is wrong because real turbines have irreversibilities, so the actual outlet enthalpy is higher than the ideal outlet enthalpy.
- Using the quality formula outside the saturated mixture region is wrong because x only applies when the state is between saturated liquid and saturated vapor.
Practice Questions
- 1 An ideal Rankine cycle has h1 = 190 kJ/kg, h2 = 194 kJ/kg, h3 = 3300 kJ/kg, and h4 = 2200 kJ/kg. Find turbine work, pump work, net work, heat input, and thermal efficiency.
- 2 A saturated steam mixture has h = 2100 kJ/kg, h_f = 700 kJ/kg, and h_fg = 2000 kJ/kg. Calculate the steam quality.
- 3 A turbine has h3 = 3400 kJ/kg, h4s = 2100 kJ/kg, and h4_actual = 2300 kJ/kg. Calculate the turbine isentropic efficiency.
- 4 Explain why increasing boiler pressure can improve Rankine cycle efficiency but may also create concerns about moisture at the turbine exit.