Rankine Cycle

The Rankine cycle is the basic model used to explain how steam power plants turn heat into work. Water is pumped as a liquid, heated into steam, expanded through a turbine, and condensed back to liquid so the loop can repeat.

What makes the cycle practical is phase change. Pumping a liquid takes much less work than compressing a gas, so the turbine can still deliver useful net work after the pump input is subtracted.

How The Rankine Cycle Works

In the pump, liquid water is compressed to a higher pressure. Because the fluid is still mostly liquid here, the pump usually needs much less work than the turbine can produce.

In the boiler, heat is added to the high-pressure liquid until it becomes steam, and often until it becomes superheated steam. This is the main heat-input stage.

In the turbine, the steam expands and does work on the turbine blades. That turbine work is the main useful output of the cycle.

In the condenser, heat is rejected so the exhaust steam becomes liquid again. Without this step, the pump would not be handling the fluid in the intended liquid state.

Ideal Rankine Cycle Assumptions

For the ideal Rankine cycle, the usual assumptions are:

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

Those assumptions make the cycle easier to analyze. Real plants do not satisfy them exactly, so real performance is lower than the ideal prediction for the same operating limits.

Rankine Cycle Efficiency Formula

The main bookkeeping relation is

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

Here $Q_{in}$ is the heat added in the boiler, $W_{turbine}$ is the turbine work output, and $W_{pump}$ is the pump work input. This is a thermal efficiency, so it tells you what fraction of the input heat becomes net work.

Use that formula only when all energy terms are written on the same basis, such as per kilogram of working fluid or per second for the whole plant.

Rankine Cycle Example

Suppose an idealized cycle is analyzed per kilogram of working fluid and gives these rounded values:

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

Then the net work is

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

So the thermal efficiency is

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

or about $29.7\%$.

This simple example shows the main idea:

• more turbine work helps efficiency
• more pump work reduces net work
• more heat input does not automatically mean better efficiency

What matters is the ratio of net work to heat supplied.

Why The Condenser Matters

Students often focus on the boiler and turbine and treat the condenser as a side detail. It is not.

The condenser lets the cycle return the fluid to a liquid state, which keeps pump work relatively small and makes the closed loop practical. It also sets an important low-temperature part of the cycle, which affects efficiency.

Common Mistakes

Mixing up the Rankine and Carnot cycles

The Carnot cycle is a theoretical benchmark with reversible isothermal heat transfer. The Rankine cycle is a more practical vapor-power model built around pumps, boilers, turbines, and condensers.

Assuming the cycle efficiency is just turbine work divided by boiler heat

The pump work must be subtracted first. The correct net work is $W_{turbine} - W_{pump}$.

Forgetting the ideal assumptions

If the turbine is not isentropic, pressure drops are significant, or the states are not what the model assumes, ideal Rankine relations will not match the real plant exactly.

Thinking every Rankine cycle has the same efficiency

Efficiency depends on operating pressures, temperatures, turbine and pump performance, and whether modifications such as superheating, reheating, or regeneration are used.

Where The Rankine Cycle Is Used

The Rankine cycle is the base model for many steam-based power systems. It is commonly used to explain coal-fired plants, nuclear steam cycles, concentrated solar thermal plants, geothermal units, and other systems where heat first makes steam and steam then drives a turbine.

It also gives a clean starting point for understanding why engineers add superheating, reheating, and feedwater heating in more advanced designs.

Try Your Own Version

Change just one number in the worked example and predict the effect before calculating. For example, keep $Q_{in}$ the same and raise $W_{turbine}$ to $1000\ \mathrm{kJ/kg}$, or keep turbine work fixed and see what happens if pump work doubles. Solving a similar case with your own numbers is the fastest way to make the cycle feel intuitive.