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Rankine cycle working principle

Short answer

The Rankine cycle is the vapor power cycle: pump raises pressure of saturated liquid isentropically, boiler adds heat at constant pressure to produce steam, turbine expands steam isentropically, and condenser rejects heat at constant pressure returning to saturated liquid.

Explain the working principle of an Rankine cycle with P-V and T-S diagram.

The Rankine cycle is the ideal vapour power cycle used in steam power plants. It removes the practical difficulties of the Carnot vapour cycle: the steam is fully condensed to liquid, so a small pump (not a compressor) can raise the pressure.

        Boiler (Q_in)
     2 +----------+ 3
       |          |
     Pump        Turbine --> W_out
       |          |
     1 +----------+ 4
       Condenser (Q_out)

Processes

  1. 1-2: Isentropic compression in the pump. Saturated liquid at the condenser pressure is pumped to the boiler pressure. The pump work, w_p = v_f (P₂ − P₁), is very small.
  2. 2-3: Constant-pressure heat addition in the boiler. The compressed liquid is heated, evaporated and (usually) superheated to state 3.
  3. 3-4: Isentropic expansion in the turbine. The steam expands to the condenser pressure and produces work. The exit is a wet mixture (or slightly superheated).
  4. 4-1: Constant-pressure heat rejection in the condenser. The wet steam condenses to saturated liquid.

Diagrams

 T-s diagram                        P-v diagram
 T                                  P
 |                       3          |  2 ____________________ 3
 |           .-'''-.   .'|          |  |                       \
 |         .'       '.'  |          |  |                        '.
 |   2'  /____________3' |          |  |                          '-.
 |      /              \ |          |  1 _________________________ 4
 |     /                \|          +----------------------------------> v
 |  2 /                  |\
 |  1/___________________4 \
 |  /                       \
 +-----------------------------> s
 (2 lies just above 1; 2'-3' boiling, 3'-3 superheating)

Energy relations (per kg)

  • w_p = h₂ − h₁
  • q_in = h₃ − h₂
  • w_t = h₃ − h₄
  • q_out = h₄ − h₁

η = [(h₃ − h₄) − (h₂ − h₁)]/(h₃ − h₂)

Efficiency improves with higher boiler pressure and temperature (superheating) and lower condenser pressure.

✓ Answer checked by Claude Opus 5.5 (high effort)

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