Thermodynamics

388 | ThermodynamicsSubstituting, the rate of entropy generation is determined to beS # gen m # 3s 3 m # 1s 1 m # 2s 2 Q# outT b 1322.7 0.18174 300 0.03609 22.7 1.74062 Btu>min # R180 Btu>min 530 R 8.65 Btu/min # RDiscussion Note that entropy is generated during this process at a rate of8.65 Btu/min · R. This entropy generation is caused by the mixing of twofluid streams (an irreversible process) and the heat transfer between themixing chamber and the surroundings through a finite temperature difference(another irreversible process).EXAMPLE 7–21Entropy Generation Associated with HeatTransferA frictionless piston–cylinder device contains a saturated liquid–vapormixture of water at 100C. During a constant-pressure process, 600 kJ ofheat is transferred to the surrounding air at 25C. As a result, part of thewater vapor contained in the cylinder condenses. Determine (a) the entropychange of the water and (b) the total entropy generation during this heattransfer process.T = 100°CH 2 O600 kJT surr = 25°CFIGURE 7–69Schematic for Example 7–21.Solution Saturated liquid–vapor mixture of water loses heat to its surroundings,and some of the vapor condenses. The entropy change of the water andthe total entropy generation are to be determined.Assumptions 1 There are no irreversibilities involved within the systemboundaries, and thus the process is internally reversible. 2 The watertemperature remains constant at 100C everywhere, including theboundaries.Analysis We first take the water in the cylinder as the system (Fig. 7–69).This is a closed system since no mass crosses the system boundary duringthe process. We note that the pressure and thus the temperature of water inthe cylinder remain constant during this process. Also, the entropy of thesystem decreases during the process because of heat loss.(a) Noting that water undergoes an internally reversible isothermal process,its entropy change can be determined from¢S system QT system600 kJ1100 273 K2 1.61 kJ /K(b) To determine the total entropy generation during this process, weconsider the extended system, which includes the water, the piston–cylinderdevice, and the region immediately outside the system that experiences a