Solved: A combined gas turbinevapor power plant operates

Chapter 9, Problem 9.98

(choose chapter or problem)

A combined gas turbine–vapor power plant operates as in Fig. 9.22. Steady-state data at principal states of the cycle are given in the table below. An air-standard analysis is assumed for the gas turbine. Air enters the compressor at \(p_{1}=14.7 \mathrm{lbf} / \mathrm{in.}^{2}, T_{1}=520^{\circ} \mathrm{R}\) and a volumetric flow rate of \(40,000 \mathrm{ft}^{3} / \mathrm{min} \text {. Also } p_{1}=p_{4}=p_{5} \text { and } p_{2}=p_{3}=12 \mathrm{~atm} \text {. }\) Except for the combustor, all components operate adiabatically. Kinetic and potential energy effects are negligible. Determine

(a) the mass flow rates of the air, steam, and cooling water, each in lb/h.

(b) the net power developed by the gas turbine cycle and the vapor cycle, respectively, each in Btu/h.

(c) the thermal efficiency of the combined cycle.

(d) a full accounting of the net exergy increase of the air passing through the combustor of the gas turbine, \(\dot{m}_{\mathrm{air}}\left[\mathrm{e}_{\mathrm{f}_{3}}-\mathrm{e}_{\mathrm{f} 2}\right]\) in Btu/h, and the exergetic efficiency of the combined cycle.

Let \(T_{0}=520^{\circ} \mathrm{R}, p_{0}=14.7 \mathrm{lbf} / \mathrm{in}^{2}\)