Question 7.229E: A small air turbine with an isentropic efficiency of 80% sho...

C.V. Turbine actual energy Eq.4.13:

Table F.5:        h _{ i }=449.794   Btu / lbm

C.V. Ideal turbine, Eq.7.27 and energy Eq.4.13:

From Table F.5:      T _{ e , s }=1232.7   R ,      s _{ Te }^{ o }=1.84217   Btu / lbm R

Entropy Eq.7.9:      s _{ i }= s _{ e , s }      adiabatic and reversible

To relate the entropy to the pressure use Eq.6.19 inverted and standard entropy from Table F.5:

If constant heat capacity was used

Eq.7.9 (adibatic and reversible) gives constant s and relation is Eq.6.23

…………………………………..

Eq.4.13 : q+h_{i}+\frac{ V _{i}^{2}}{2}+g Z_{i}=h_{e}+\frac{ V _{e}^{2}}{2}+g Z_{e}+w

Eq.7.27 : \eta_{\text {turbine }}=\frac{w}{w_{s}}=\frac{h_{i}-h_{e}}{h_{i}-h_{e s}}

Eq.7.9 : s_{e}=s_{i}+\sum \frac{q}{T}+s_{\text {gen }}

Eq. 6.19 : s_{2}-s_{1}=\left(s_{T 2}^{0}-s_{T 1}^{0}\right)-R \ln \frac{P_{2}}{P_{1}}

Eq.6.23 : \frac{T_{2}}{T_{1}}=\left(\frac{P_{2}}{P_{1}}\right)^{(k-1) / k}