Chapter 7, Problem 7.22P

Interpretation Introduction

Interpretation:

In an adiabatic turbine for ideal gas with constant heat capacity find out turbine efficiency for $T_1=500{\text{ K, P}}_1={\text{6 bar, T}}_2=371{\text{ K, P}}_2=1.2{\text{ bar, C}}_p/R=7/2$

Concept introduction:

For a steady state adiabatic gas turbine, its in and out pressures are fixed. Hence, an isentropic process of turbine is called idealized process. There is no heat transfer occur in the turbine, which indicates that work output is the desired output from a turbine.

Enthalpy for ideal gas with constant heat capacity can be written by formula:

  $\Delta H=C_P\left(T_2-T_1\right)$

Enthalpy due to expansion:

  $\Delta H_s=C_P{T}_1\left[{\left(\frac{P_2}{P_1}\right)}^{\frac{R}{C_P}}-1\right]$

Efficiency $\eta =\frac{\Delta H}{\Delta H_s}$