Figure P13.111 shows a simple vapor power plant. The fuel

Chapter 13, Problem 13.111

(choose chapter or problem)

Figure P13.111 shows a simple vapor power plant. The fuel is methane that enters at \(77^{\circ} \mathrm{F}\), 1 atm and burns completely with 200% theoretical air entering at \(77^{\circ} \mathrm{F}\), 1 atm. Steam exits the steam generator at \(900^{\circ} \mathrm{F}\), \(500 \mathrm{lbf} / \mathrm{in} ^{2}\) The vapor expands through the turbine and exits at \(1 \mathrm{lbf} / \mathrm{in} .^{2}\), and a quality of 97%. At the condenser exit, the pressure is 1 lbf/in.2 and the water is a saturated liquid. The plant operates at steady state with no stray heat transfers from any plant component. Pump work and the effects of motion and gravity are negligible. Determine

(a) the balanced reaction equation.

(b) the vapor mass flow rate, in lb per lbmol of fuel.

(c) the cooling water mass flow rate, in lb per lbmol of fuel.

(d) each of the following, expressed as a percent of the exergy entering the steam generator with the fuel, (i) the exergy exiting with the stack gases, (ii) the exergy destroyed in the steam generator, (iii) the power developed by the turbine, (iv) the exergy destroyed in the turbine, (v) the exergy exiting with the cooling water, (vi) the exergy destroyed in the condenser.

Base exergy values on the environment of Table A-26 (Model II) and assume all water present in the combustion products is a vapor at the dead state.