Why is the turbine leg vertical on T–s?

The ideal turbine is modeled as reversible adiabatic (isentropic) expansion, so specific entropy stays constant while temperature drops— a vertical segment in the s–T plane.

Why does P–v look like a skewed rectangle?

Liquid specific volume changes little in the pump, while vapor volumes are much larger. The sketch exaggerates the contrast for clarity; real cycles use property software or steam tables.

Is η (diagram proxy) the real thermal efficiency?

No. It is a rough ratio built from the schematic polygon in normalized T–s units. Real efficiency needs enthalpies from accurate property data and accounts for irreversibilities in the turbine and pump.

Rankine Cycle (Steam)

The ideal Rankine cycle models a steam power plant: feedwater is pumped to boiler pressure (small enthalpy rise), heat is added at nearly constant pressure through preheat, evaporation under the vapor dome, and optional superheat; the turbine expands steam isentropically (vertical on T–s); the condenser rejects heat at low pressure, often returning saturated liquid. This page uses the same schematic vapor dome as the wet-steam lab: normalized pressure sliders set condenser and boiler saturation levels, and turbine outlet quality x₄ fixes the expansion entropy so state 4 lies on the low-pressure isobar. A second view sketches a qualitative P–v loop driven by the same sliders—specific volumes are not from steam tables. Efficiency numbers labeled “diagram proxy” are illustrative ratios of areas in normalized coordinates, not plant performance.

Who it's for: Engineering thermodynamics students comparing heat-engine cycles; complements Carnot, Otto, Diesel, and Stirling simulators.

Key terms

Rankine cycle
T–s diagram
vapor dome
turbine quality
isobaric heat addition
isentropic expansion
condenser

How it works

Steam plant idealization on T–s with the vapor dome: pump, boiler, turbine, condenser. Optional qualitative P–v loop for the same sliders.

Key equations

Ideal: q_in = h₃ − h₂, q_out = h₄ − h₁, w_t = h₃ − h₄, w_p = h₂ − h₁ · η = w_net / q_in

Isentropic turbine: s₃ = s₄ · Wet exhaust: s₄ = (1−x₄) s_f + x₄ s_g at ṕ_cond

Frequently asked questions

Why is the turbine leg vertical on T–s?: The ideal turbine is modeled as reversible adiabatic (isentropic) expansion, so specific entropy stays constant while temperature drops— a vertical segment in the s–T plane.
Why does P–v look like a skewed rectangle?: Liquid specific volume changes little in the pump, while vapor volumes are much larger. The sketch exaggerates the contrast for clarity; real cycles use property software or steam tables.
Is η (diagram proxy) the real thermal efficiency?: No. It is a rough ratio built from the schematic polygon in normalized T–s units. Real efficiency needs enthalpies from accurate property data and accounts for irreversibilities in the turbine and pump.

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