# Rankine Cycle - Ideal Rankine Cycle Efficiency

## Rankine Cycle Efficiency

**Rankine cycle** is a condensation process where steam is to be condensed into water.

Rankine cycle is nothing but a modification of Carnot cycle. Ideal Rankine cycle is very useful in steam power plants and gas power plants. To improve the efficiency of Rankine cycle in the steam power plant, there are some changes in Rankine cycle which differs from the Carnot cycle. Firstly, a pump is used in place of condenser to handle only liquid, not a mixture of liquid and vapour.Secondly, exhaust steam from the turbine is completely condensed in the condenser, see in the following diagram:

It is a reversible process. The **Rankine cycle efficiency** is much higher than Carnot cycle efficiency as because the pump
is used in the Rankine cycle, which gives higher work ratio by doing significant proportion of turbine work.

A simple * Rankine cycle* is completed by following four processes. Steam is used as a working substance in Rankine cycle, is shown
the above p-v Rankine cycle diagram and T-s Rankine cycle diagram.

1).Process 1-2:

As we see in the above diaqgram, saturated water coming from hot well ata point 1 is isothyermally converted into dry saturated
steam in a boiler and heat is absorbed at constant temperature T_{1} and pressure p_{1}. The steam is now dry
condition showing at point 2. The temperature and pressure at point 2 is T_{2} and p_{2} respectively. It is
similar to the T_{1} and p_{1}. This isothermal expansion process shown in the p-v and T-s curve 1-2. During
isothermal expansion process, the heat absorbed by water denotes h_{fg1} which is similar to the h_{fg2} as
a corresponding pressure p_{1} and p_{2}.(since p_{1} = p_{2})

2).Process 2-3:

Now the dry saturated steam enters into the turbine. Here steam expands isentropically and the pressure and temperature falls down from p_{2} to p_{3} and T_{2} to T_{3} with a dryness fraction x_{3}. During
this expansion, no heat is supplied or rejected. So, there is no change in entropy and curve from 2-3 falls down show the
above graph.

3).Process 3-4:

At this stage, Wet steam enters the condenser for condensation of steam. Heat is rejected in the condenser at a constant
temperature T_{3} and pressure p_{3} until the total steam is condensed into water. At point 4 conditions,
T_{3} = T_{4}. So the curve of the p-v and T-s diagram is straight line and heat is rejected by steam is
called latent heat equal to x_{3hfg3}

4).Process 4-1:

Now water enters to the boiler at point 4 positions for warming. In the boiler, water is heated to a constant temperature
T_{4} to T_{1} and volume. The pressure rises from p_{4} to p_{1}. This operation is shown in the graph 4-1 on p-v and T-s diagram. The heat
absorbed by water during this operation is equal to the sensible heat or liquid heat corresponding to the pressure p_{1} which is equal to sensible heat at point 1 minus sensible heat at point 4

Let,

h_{f1} = h_{f2} = Senseble heat or enthalpy of water at point 1 corresponding pressure p_{1} or
p_{2} (since p_{1} = p_{2})

h_{f4} = h_{f3} = Senseble heat or enthalpy of water at point 4 corresponding pressure p_{4} or
p_{3} (since p_{4} = p_{3})

So, Heat absorbed at warmed operation 4-1 = h_{f1} = h_{f4} = h_{f2} = h_{f3}

and heat absorbed during the complete cycle is

= h_{fg2} + (h_{f2} - h_{f3}) = h_{f2} + h_{fg2} - h_{f3} = h_{f2} - h_{f3}

We know that heat rejected during the cycle

= h_{3} - h_{f4} = h_{f3} + x_{3}h_{fg3} - h_{f4} = x_{3}h_{fg3}

Worhdone during the cycle is = Heat absorbed - heat rejected

= (h_{2} - h_{f3}) - x_{3}h_{fg3}

= h_{2} - (h_{f3} + x_{3}h_{fg3})

= h_{2} - h_{3}

So, rankine cycle efficiency η_{R} is -

**☛ Read More Questions**Click here