Thermodynamics

176 | ThermodynamicsUse actual data from the experimentshown here to verify the first law ofthermodynamics. See end-of-chapterproblem 4–178.© Ronald MullisenQ – W otherEXPERIMENTP = const.∆H– W b = ∆UQ – W other = ∆H(b) The only other form of work in this case is the electrical work, which canbe determined fromState 1:W e VI¢t 1120 V2 10.2 A2 1300 s2 a1 kJ>sb 7.2 kJ1000 VAThe enthalpy at the final state can be determined directly from Eq. 4–18 byexpressing heat transfer from the system and work done on the system asnegative quantities (since their directions are opposite to the assumed directions).Alternately, we can use the general energy balance relation with thesimplification that the boundary work is considered automatically by replacingU by H for a constant-pressure expansion or compression process:Net energy transferby heat, work, and massW e,in Q out W b ¢UChange in internal, kinetic,potential, etc., energiesNow the final state is completely specified since we know both the pressureand the enthalpy. The temperature at this state isState 2:P 1 300 kPafhsat. vapor1 h g @ 300 kPa 2724.9 kJ>kg1Table A–52E in E out W e,in Q out ¢H m 1h 2 h 1 21since P constant27.2 kJ 3.7 kJ 10.025 kg2 1h 2 2724.92 kJ>kgh 2 2864.9 kJ>kg¢E system⎫ ⎪⎬⎪⎭⎫⎪⎬⎪⎭P 2 300 kPah 2 2864.9 kJ>kg fT 2 200°C1Table A–62Therefore, the steam will be at 200°C at the end of this process.Discussion Strictly speaking, the potential energy change of the steam isnot zero for this process since the center of gravity of the steam rose somewhat.Assuming an elevation change of 1 m (which is rather unlikely), thechange in the potential energy of the steam would be 0.0002 kJ, which isvery small compared to the other terms in the first-law relation. Therefore, inproblems of this kind, the potential energy term is always neglected.FIGURE 4–14For a closed system undergoing aquasi-equilibrium, P constantprocess, U W b H.EXAMPLE 4–6Unrestrained Expansion of WaterA rigid tank is divided into two equal parts by a partition. Initially, one side ofthe tank contains 5 kg of water at 200 kPa and 25°C, and the other side isevacuated. The partition is then removed, and the water expands into the entiretank. The water is allowed to exchange heat with its surroundings until the temperaturein the tank returns to the initial value of 25°C. Determine (a) the volumeof the tank, (b) the final pressure, and (c) the heat transfer for this process.Solution One half of a rigid tank is filled with liquid water while the otherside is evacuated. The partition between the two parts is removed andwater is allowed to expand and fill the entire tank while the temperature ismaintained constant. The volume of tank, the final pressure, and the heattransfer are to be to determined.