Thermodynamics

Chapter 4 | 169EXAMPLE 4–2Boundary Work for a Constant-Pressure ProcessA frictionless piston–cylinder device contains 10 lbm of steam at 60 psiaand 320F. Heat is now transferred to the steam until the temperaturereaches 400F. If the piston is not attached to a shaft and its mass is constant,determine the work done by the steam during this process.Solution Steam in a piston cylinder device is heated and the temperaturerises at constant pressure. The boundary work done is to be determined.Analysis A sketch of the system and the P-v diagram of the process areshown in Fig. 4–7.Assumption The expansion process is quasi-equilibrium.Analysis Even though it is not explicitly stated, the pressure of the steamwithin the cylinder remains constant during this process since both theatmospheric pressure and the weight of the piston remain constant. Therefore,this is a constant-pressure process, and, from Eq. 4–2or(4–6)since V mv. From the superheated vapor table (Table A–6E), the specificvolumes are determined to be v 1 7.4863 ft 3 /lbm at state 1 (60 psia,320F) and v 2 8.3548 ft 3 /lbm at state 2 (60 psia, 400F). Substitutingthese values yieldsW b 110 lbm2 160 psia2318.3548 7.48632 ft 3 1 Btu>lbm4 a5.404 psia # b ft3 96.4 Btu22W b P dV P 0 dV P 0 1V 2 V 1 211W b mP 0 1v 2 v 1 2Discussion The positive sign indicates that the work is done by thesystem. That is, the steam used 96.4 Btu of its energy to do this work. Themagnitude of this work could also be determined by calculating the area underthe process curve on the P-V diagram, which is simply P 0 V for this case.P, psia601P 0 = 60 psia2H 2 Om = 10 lbmP = 60 psiaHeatv 1 = 7.4863Area = w bv 2 = 8.3548v, ft 3 /lbmFIGURE 4–7Schematic and P-v diagram forExample 4–2.