Thermodynamics

790 | Thermodynamicsthis fuel mixture. Determine (a) the theoretical air–fuel ratiofor this reaction; (b) the product–fuel ratio for this reaction;(c) the air-flow rate for a fuel mixture flow rate of 5 kg/s; and(d) the lower heating value of the fuel mixture with 200 percenttheoretical air at 25°C. Answers: (a) 14.83 kg air/kg fuel,(b) 30.54 kg product/kg fuel, (c) 148.3 kg/s, (d) 43,672 kJ/kg fuel15–106 The furnace of a particular power plant can be consideredto consist of two chambers: an adiabatic combustionchamber where the fuel is burned completely and adiabatically,and a heat exchanger where heat is transferred to aCarnot heat engine isothermally. The combustion gases in theheat exchanger are well-mixed so that the heat exchanger isat a uniform temperature at all times that is equal to the temperatureof the exiting product gases, T p . The work output ofthe Carnot heat engine can be expressed asW Qh C Q a 1 T 0T pbwhere Q is the magnitude of the heat transfer to the heatengine and T 0 is the temperature of the environment. Thework output of the Carnot engine will be zero either whenT p T af (which means the product gases will enter and exitthe heat exchanger at the adiabatic flame temperature T af , andthus Q 0) or when T p T 0 (which means the temperatureFuelAirAdiabaticcombustionchamberof the product gases in the heat exchanger will be T 0 , andthus h C 0), and will reach a maximum somewhere inbetween. Treating the combustion products as ideal gaseswith constant specific heats and assuming no change in theircomposition in the heat exchanger, show that the work outputof the Carnot heat engine will be maximum whenT p 2T af T 0Also, show that the maximum work output of the Carnotengine in this case becomes2T 0W max CT af a 1 b B T afwhere C is a constant whose value depends on the compositionof the product gases and their specific heats.15–107 The furnace of a particular power plant can be consideredto consist of two chambers: an adiabatic combustionchamber where the fuel is burned completely and adiabaticallyand a counterflow heat exchanger where heat is transferredto a reversible heat engine. The mass flow rate of theworking fluid of the heat engine is such that the workingfluid is heated from T 0 (the temperature of the environment)to T af (the adiabatic flame temperature) while the combustionproducts are cooled from T af to T 0 . Treating the combustionproducts as ideal gases with constant specific heats andassuming no change in their composition in the heatexchanger, show that the work output of this reversible heatengine isW CT 0 a T afT 0 1 ln T afT 0bT 0T pAdiabaticHeatexchangerT p = const.QFuelAircombustionchamberHeatexchangerT afT 0T 0T 0FIGURE P15–107WWSurroundingsT 0SurroundingsT 0FIGURE P15–106