8.17 Water is the working fluid in a Rankine cycle. Superheated vapor enters the turbine at 10 MPa, 4808C, and the condenser pressure is 6 kPa. The turbine and pump have isentropic efficiencies of 80 and 70%, respectively. Determine for the cycle (a) the heat transfer to the working fluid passing through the steam generator, in kJ per kg of steam flowing. (b) the thermal efficiency. (c) the heat transfer from the working fluid passing through the condenser to the cooling water, in kJ per kg of steam flowing.

a) The Heat Transfer  to the working fluid passing through the steam generator is 3153.3 KJ/Kg

b) The Thermal Efficiency is 32.7%.

c) The heat transfer from the working fluid passing through the condenser to the cooling water is 2121 KJ/Kg

Explanation:

Given,

P1=10MPa

P2=6kPa

h1=3320 KJ/Kg and s1= 6530J/Kgk due to the properties of water at 10MPa.

h2=20100 KJ/Kg, s2=s1= 6530J/Kgk and quality, x=0.77 due to the properties at 6kPa.

h3=151 KJ/Kg, s3= 521J/Kgk and v3=0.00101 due to the properties at P3=P2=6kPa and x=0.

h4=162 KJ/Kg, s4=s3= 521J/Kgk and v4=0.001 due to the properties at P4=P1=10MPa.

The efficiency of turbine is 0.8.

So,( h1-h2')/(h1-h2) =0.8

By solving above equation:

h2'=2272KJ/Kg

The efficiency of pump is 0.7.

So,( h4-h3)/(h4'-h3) =0.7

By solving above equation:

h4'=166.71KJ/Kg

a) The Heat Transfer  to the working fluid passing through the steam generator:

q=h1-h4'

q=3320 -166.7

q= 3153.3 KJ/Kg

b) Thermal Efficiency:

=(h1-h2')-(h4'-h3)/q

= 32.7%

c) The heat transfer from the working fluid passing through the condenser to the cooling water:

=h2'-h3

=2121KJ/Kg

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