Question

A gas turbine is supplied with an ideal gas mixture having the following gravimetric analysis: 19% Argon, 10% Helium, and 71% Neon at 500 K, and 0.3 MPa. Products exit the turbine at 350 K, and 0.11 MPa. Assuming an isentropic turbine, what is the work developed by the turbine per kilogram of gas mixture?

Answer 1

Answer:

The work developed is 202.4 $\frac{kJ}{kg}$

Explanation:

First, write the energy balance equation:

$W=H_{1}-H_{2}=m*(h_{1}-h_{2})$

The enthalpy change for an ideal gas is just function of its temperature, so the pressure changes are not relevant; the enthalpy change of an ideal gas may be calculated as:

$dh=CpdT$

Assuming Cp constant,

$h_{2}-h_{1}=Cp(T_{2}-T_{1})$

The average Cp is then calculated with data from van Wylen table A.6 with a simple mix rule based on molar fractions:

$Cp_{av}=0.52*0.19+5.193*0.1+0.71*1.03=1.3494kJ/kg$

$h_{2}-h_{1}=1.3494*(350-500)=-202.41\frac{kJ}{kg}$

$W=202.41\frac{kJ}{kg}$