Answer to Question #214836 in Molecular Physics | Thermodynamics for Wavie

Question

In a gas turbine unit air is drawn in at 1.02 bar and 15°C, and is compressed to 6.12 bar. Calculate the thermal efficiency and the work ratio of the ideal constant pressure cycle, when the maximum cycle temperature is 800°C.

Answer 1

$\eta=1-\frac 1{r_p^{\frac{\gamma-1}{\gamma}}}=1-(\frac{1.02}{6.12})^{\frac{1.4-1}{1.4}}=0.401=40.1\%,$

$\frac{T_2}{T_2}=\frac{T_3}{T_4}=(\frac{p_2}{p_1})^{\frac{\gamma-1}{\gamma}}=1.669,$

$T_2=1.669T_1=480.5~K,$

$T_4=\frac{T_3}{1.669}=642.9~K,$

$NWO=c_p(T_3-T_4)-c_p(T_2-T_1)=238.8~\frac{kJ}{kg},$

$GWO=c_p(T_3-T_4)=432.3~\frac{kJ}{kg},$

$WR=\frac{NWO}{GWO}=0.553=55.3~\%.$