Chapter 4.8, Problem 10P

Interpretation Introduction

Interpretation:

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.

$\frac{d\left(M\widehat{S}\right)}{dt}={\displaystyle \sum _{j=1}^{j=J}{\dot{m}}_{j,in}{\widehat{S}}_j}-{\displaystyle \sum _{k=1}^{k=K}{\dot{m}}_{k,out}{\widehat{S}}_k}+{\displaystyle \sum _{n=1}^{n=N}\frac{{\dot{Q}}_n}{T_n}}+{\dot{S}}_{gen}$

Here, time taken is t, mass of the system is M, specific entropy of the system are $\widehat{S}$, mass flow rates of individual streams entering and leaving the system are ${\dot{m}}_{j,in}$ and ${\dot{m}}_{k,out}$, specific entropies of streams entering and leaving the system are ${\widehat{S}}_j$ and ${\widehat{S}}_k$, actual rate at which heat is added to or removed from the system at one particular location is ${\dot{Q}}_n$, the temperature of the system at the boundary where the heat transfer labelled n occurs is $T_n$, and the rate at which entropy is generated within the boundaries of the system is ${\dot{S}}_{gen}$.

Write an energy balance for an adiabatic steady state turbine.

$\frac{{\dot{W}}_S}{\dot{m}}={\widehat{H}}_{out}-{\widehat{H}}_{in}$

Here, specific enthalpy at inlet and outlet are ${\widehat{H}}_{in}$ and ${\widehat{H}}_{out}$, mass flow rate is $\dot{m}$, and rate at which shaft work is added to the system is ${\dot{W}}_S$.

Write the efficiency of the turbine.

$\eta =\frac{\frac{{\dot{W}}_{S,actual}}{\dot{m}}}{\frac{{\dot{W}}_{S,rev}}{\dot{m}}}$

Here, actual work done by the shaft is ${\dot{W}}_{S,actual}$ and reversible work done by the shaft is ${\dot{W}}_{S,rev}$.