Rankine Cycle

When you analyze a steam power plant, the goal is usually one number: how much of the input heat becomes useful work. The Rankine cycle gives you a repeatable procedure to get there. Water is pumped as a liquid, boiled into steam, expanded through a turbine, and condensed back to liquid so the loop repeats, and you account for energy at each stage.

The reason the cycle works at all is phase change: pumping a liquid takes far less work than compressing a gas, so the turbine still delivers useful net work after the pump input is subtracted.

When This Procedure Applies

Use the Rankine analysis for vapor-power systems where heat first makes steam and steam then drives a turbine, coal-fired plants, nuclear steam cycles, concentrated solar thermal plants, and geothermal units. If the working fluid changes phase between a liquid pump and a vapor turbine in a closed loop, this is the right model.

The Procedure, Step By Step

1. Identify the four main devices

Trace the fluid through each component and name what it does:

• Pump: compresses liquid water to high pressure; because the fluid is still mostly liquid, this usually needs much less work than the turbine produces.
• Boiler: adds heat to the high-pressure liquid until it becomes steam, often superheated. This is the main heat-input stage.
• Turbine: lets the steam expand and do work on the blades. This is the main useful output.
• Condenser: rejects heat so the exhaust steam becomes liquid again, returning the fluid to the state the pump expects.

2. Check the ideal assumptions

For the ideal Rankine cycle, the usual assumptions are:

• the pump and turbine are isentropic
• heat addition in the boiler is at constant pressure
• heat rejection in the condenser is at constant pressure
• pressure drops in pipes and heat exchangers are neglected

These make the analysis tractable. Real plants do not satisfy them exactly, so real performance is lower than the ideal prediction for the same operating limits.

3. Track energy per unit mass

Put every energy term on the same basis, such as per kilogram of working fluid or per second for the whole plant, then apply the efficiency relation:

$$\eta_{th} = \frac{W_{net}}{Q_{in}} = \frac{W_{turbine} - W_{pump}}{Q_{in}}$$

Here $Q_{in}$ is boiler heat added, $W_{turbine}$ is turbine work out, and $W_{pump}$ is pump work in. This thermal efficiency is the fraction of input heat that becomes net work, and it is valid only when all terms share one basis.

4. Interpret the result physically

Read what the number says about the design, not just the arithmetic.

Full Worked Example

Analyze an idealized cycle per kilogram of working fluid with these rounded values:

• turbine work output: $W_{turbine} = 900\ \mathrm{kJ/kg}$
• pump work input: $W_{pump} = 10\ \mathrm{kJ/kg}$
• boiler heat input: $Q_{in} = 3000\ \mathrm{kJ/kg}$

Step 3 gives the net work,

$$W_{net} = 900 - 10 = 890\ \mathrm{kJ/kg}$$

and the thermal efficiency,

$$\eta_{th} = \frac{890}{3000} \approx 0.297$$

or about $29.7\%$. Step 4 reads the physics: more turbine work helps efficiency, more pump work reduces net work, and more heat input does not automatically raise efficiency. What matters is the ratio of net work to heat supplied.

This is also why the condenser is not a side detail. By returning the fluid to liquid, it keeps pump work small and makes the closed loop practical, and it sets an important low-temperature part of the cycle that affects efficiency.

Where Students Get Stuck, And How To Check

• Confusing Rankine with Carnot. Carnot is a reversible benchmark with isothermal heat transfer; Rankine is a practical vapor-power model built around pumps, boilers, turbines, and condensers.
• Forgetting to subtract pump work. Efficiency is not turbine work over boiler heat; net work is $W_{turbine} - W_{pump}$ (step 3).
• Ignoring the ideal assumptions. If the turbine is not isentropic or pressure drops are significant, ideal relations will not match the real plant. Recheck step 2.
• Assuming every cycle has the same efficiency. It depends on operating pressures, temperatures, component performance, and modifications such as superheating, reheating, or regeneration.

Where the Rankine Cycle Is Used

Beyond the plants above, it gives a clean starting point for understanding why engineers add superheating, reheating, and feedwater heating in more advanced designs.

Practice the Procedure

Change just one number in the worked example and predict the effect before recalculating: keep $Q_{in}$ fixed and raise $W_{turbine}$ to $1000\ \mathrm{kJ/kg}$, or hold turbine work and double the pump work. Rerunning steps 3 and 4 on your own numbers is the fastest way to make the cycle intuitive.