Fundamentals of Chemical Engineeri...

1st Edition
Kevin D. Dahm + 1 other
ISBN: 9781111580704



Fundamentals of Chemical Engineeri...

1st Edition
Kevin D. Dahm + 1 other
ISBN: 9781111580704
Textbook Problem

A series of two turbines and a heat exchanger are used to obtain shaft work from steam in a steady-state process. The steam enters the first turbine at 10 bar and 250°C, and exits the turbine at 3 bar. In the heat exchanger, the steam is heated back up to 250°C, while the pressure remains 3 bar. This steam enters the second turbine in which it is expanded to 1 bar. Each turbine has an efficiency of 80%. For each kilogram of steam entering the process, find the amount of work produced in each turbine, and the amount of heat added in the heat exchanger.

Interpretation Introduction


Determine the work produced in first and second turbine and the amount of heat added to the heat exchanger.

Concept Introduction:

The expression for an entropy balance equation.


Here, time taken is t, mass of the system is M, specific entropy of the system are S^, mass flow rates of individual streams entering and leaving the system are m˙j,in and m˙k,out, specific entropies of streams entering and leaving the system are S^j and S^k, actual rate at which heat is added to or removed from the system at one particular location is Q˙n, the temperature of the system at the boundary where the heat transfer labelled n occurs is Tn, and the rate at which entropy is generated within the boundaries of the system is S˙gen.

Write an energy balance for an adiabatic steady state turbine.


Here, specific enthalpy at inlet and outlet are H^in and H^out, mass flow rate is m˙, and rate at which shaft work is added to the system is W˙S.

Write the efficiency of the turbine.


Here, actual work done by the shaft is W˙S,actual and reversible work done by the shaft is W˙S,rev.


Given information:

First turbine pressure and temperature is 10 bar and 250 degree Celsius.

Second turbine pressure and temperature is 3 bar and 250 degree Celsius with efficiency of 80%.

Refer the Appendix table A-3, “Superheated steam”, obtain the value of inlet properties of specific enthalpy and specific entropy at a pressure of 10 bar and temperature of 250°C respectively.


Calculate the inlet entropy using entropy balance equation.

d(MS^)dt=j=1j=Jm˙j,inS^jk=1k=Km˙k,outS^k+n=1n=NQ˙nTn+S˙gen        (1)

Rewrite the steady state entropy balance equation for an adiabatic ideal mass system 0=m˙inS^inm˙outS^out+S˙gen0=S^inS^out+0S^in=S^out        (2)

Substitute 6.9265kJ/kgK for S^in in Equation (2).


Refer the Appendix table A-1, “Saturated steam-pressure increments”, obtain the specific entropy and specific enthalpy for liquid and vapor state at a pressure of 3 bar.


Calculate the specific entropy of an outlet for a reversible process.

S^out,rev=(1qrev)S^L+qrevS^V        (3)

Here, mole fraction of the system for reversible process is qrev.

Substitute 1.6717kJ/kgK for S^L, 6.9916kJ/kgK for S^V, and 6.9265kJ/kgK for S^out in Equation (3).


Calculate the enthalpy for outlet steam in reversible process.

H^out,rev=(1qrev)H^L+qrevH^V        (4)

Substitute 561.4kJ/kg for H^L, 2724.9kJ/kg for H^V, and 0.988 for qrev in Equation (4)


Calculate the work done for an adiabatic steady state turbine.

W˙Sm˙=H^outH^in        (5)

Substitute 2698.4kJ/kg for H^out,rev and 2724.9kJ/kg for H^in in Equation (5).


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