Question

 Consider steam in an ideal Rankine cycle. The saturated vapor enters the turbine at 8.0 MPa. Saturated liquid exits the condenser at P = 0.008 MPa. The net power output of the cycle is 100 MW.

determine the thermal efficiency of the cycle

Answer 1

 consider the diagram below:

the processes in the cycles are:

• 1 → 2: isentropic pumping process in the pump,

• 2 → 3: isobaric heat transfer in the boiler,

• 3 → 4: isentropic expansion in the turbine, 

• 4 → 1: isobaric heat transfer in the condenser

At the turbine inlet, we have P₃ = 8.0 MPa, and X₃ = 1 (saturated steam). This gives two properties from the tables to fix the state, so that

State 4 has P4 = 0.008 MPa and s4 = s3 = 5.7432 kJ/kg/K, so the state is fixed. From the saturation tables, we can find that:

the quality of steam at state 4 is between 0 and 1 and we can use the tables to find the enthalpy as shown below: 

 

State 1 is saturated liquid at 0.008 MPa, so X1 = 0, P1 = 0.008 MPa. We then get h1 = hf = 173.88 kJ/kg, V1 = vf = 0.0010084 m3/kg. state 2 is fixed by the boiler pressure and s2 = s1. But this requires the use of the sparse compressed liquid tables. Alternatively, the pump work is easily approximated by assuming an incompressible fluid so that

The net power is

The energy input is

the thermal efficiency can therefore be determined by:

= 0.371

The thermal efficiency is given by 0.371/37.1%