Thermodynamics

454 | Thermodynamics(a) Noting that no energy enters or leaves the system during the process, theapplication of the energy balance givesE in E out ¢E systemNet energy transferby heat, work, and massChange in internal, kinetic,potential, etc., energiesBy using the specific-heat values for water and iron at room temperature(from Table A–3), the final equilibrium temperature T f becomeswhich yields⎫⎪⎬⎪⎭⎫⎪⎬⎪⎭0 ¢U0 1¢U2 iron 1¢U2 water0 3mc 1T f T i 24 iron 3mc 1T f T i 24 water0 15 kg210.45 kJ>kg # °C21Tf 350°C2 1100 kg214.18 kJ>kg # °C21Tf 30°C2T f 31.7°C(b) Exergy X is an extensive property, and the exergy of a composite systemat a specified state is the sum of the exergies of the components of that systemat that state. It is determined from Eq. 8–15, which for an incompressiblesubstance reduces to¡0X 1U U 0 2 T 0 1S S 0 2 P 0 1V V 02 mc 1T T 0 2 T 0 mc ln T T 0 0where T is the temperature at the specified state and T 0 is the temperatureof the surroundings. At the initial state,X 1,iron 15 kg2 10.45 kJ>kg # K2c1623 2932 K 1293 K2 ln623 K293 K d 245.2 kJX 1,water 1100 kg2 14.18 kJ>kg # K2c1303 2932 K 1293 K2 ln303 K293 K d 69.8 kJ mc a T T 0 T 0 ln T T 0bX 1,total X 1,iron X 1,water 1245.2 69.82kJ 315 kJSimilarly, the total exergy at the final state isX 2,iron 0.5 kJX 2,water 95.1 kJX 2,total X 2,iron X 2,water 0.5 95.1 95.6 kJThat is, the exergy of the combined system (water iron) decreased from315 to 95.6 kJ as a result of this irreversible heat transfer process.