Answer to Question #255757 in Molecular Physics | Thermodynamics for Ahmed

Question

A gas turbine receives gases from the combustion chamber at 7 bar and

650°C, with a velocity of 9 m/s. The gases leave the turbine at 1 bar with a

velocity of 45 m/s. Assuming that the expansion is Adiabatic and reversible

in the ideal gas,

calculate the power Output per unit mass flow rate,

1=1.333, Cp=1.11 KJ/Kg.K

Answer 1

We know that

$\dot{W}=\dot{m}[(c_p(T_2-T_1)+\frac{(c^2_2-c^2_1)}{2}]$

$\frac{T_1}{T_2}=(\frac{P_2}{P_2})^\frac{\gamma-1}{\gamma}$

$T_2=\frac{T_1}{1.626}=567.7K$

$T_1=650+273=923K$

$\dot{W}=1\times1.11\times(567.7-923)+\frac{45^2-9^2}{2\times10^3}$

$\dot{W}=-394.4+0.97$ =-393.4KW