Question 6.16: Problem: Air enters a gas turbine at 1100 K and 800 kPa with...

Problem: Air enters a gas turbine at 1100 K and 800 kPa with a velocity of 80 m / s. Determine the exergy of the air at the inlet to the turbine. Assume the atmosphere is at 300 K and 100 kPa.

Find: Flow exergy ψ of the air at the turbine inlet.

Known: Air pressure P = 800 kPa, air temperature T = 1100 K, air velocity V = 80 m / s, atmospheric pressure P_o = 100 kPa, atmospheric temperature T_o = 300 K.

Assumptions: Air is an ideal gas, negligible contribution from potential energy.

Properties: Air has gas constant R = 0.2870 kJ / kgK (Appendix 1), specific enthalpy at 1100 K h(1100 K) = 1161.07 kJ / kg (Appendix 7), specific enthalpy h(300 K) = 300.19 kJ / kg (Appendix 7), specific entropy sº (1100 K) = 3.07732 kJ / kgK (Appendix 7), specific entropy sº (300 K) = 1.70203 kJ / kgK (Appendix 7).

Governing equations:

Flow exergy per unit mass                          \psi =(h-h_o) – T_o (s-s_o) + \frac{\pmb{V}^2}{2} +\underbrace{gz}_{=0} 

Entropy change (ideal gas)                        \Delta s =s^\circ (T_2)-s^\circ (T_1)-R \ln \frac{P_s}{P_1}