Thermodynamics

430 | ThermodynamicsIRON200°C27°CQ inAnalysis We take the iron block as the system. This is a closed systemsince no mass crosses the system boundary. We note that heat is lost fromthe system.It probably came as a surprise to you that we are asking to find the“reversible work” for a process that does not involve any work interactions.Well, even if no attempt is made to produce work during this process, thepotential to do work still exists, and the reversible work is a quantitativemeasure of this potential.The reversible work in this case is determined by considering a series ofimaginary reversible heat engines operating between the source (at a variabletemperature T ) and the sink (at a constant temperature T 0 ), as shown inFig. 8–13. Summing their work output:anddW rev h th,rev dQ in a 1 T sinkT sourceb dQ in a 1 T 0T b dQ inRev.HEW revW rev a 1 T 0T b dQ inThe source temperature T changes from T 1 200°C 473 K to T 0 27°C 300 K during this process. A relation for the differential heat transfer from theiron block can be obtained from the differential form of the energy balanceapplied on the iron block,dE in dE out dE systemSurroundings27°CFIGURE 8–13An irreversible heat transfer processcan be made reversible by the use of areversible heat engine.Then,Net energy transferby heat, work, and mass⎫⎪⎪⎬⎪⎪⎭⎫⎪⎬⎪⎭Change in internal, kinetic,potential, etc., energiesdQ out dU mc avg dTdQ in,heat engine dQ out,system mc avg dTsince heat transfers from the iron and to the heat engine are equal in magnitudeand opposite in direction. Substituting and performing the integration,the reversible work is determined to beW rev T 0a 1 T 0T b1mc avg dT2 mc avg 1T 1 T 0 2 mc avg T 0 ln T 1TT 01 1500 kg210.45 kJ>kg # K2c1473 3002 K 1300 K2 ln473 K300 K d 8191 kJwhere the specific heat value is obtained from Table A–3. The first term inthe above equation [Q mc avg (T 1 T 0 ) 38,925 kJ] is the total heattransfer from the iron block to the heat engine. The reversible work for thisproblem is found to be 8191 kJ, which means that 8191 (21 percent) of the38,925 kJ of heat transferred from the iron block to the ambient air couldhave been converted to work. If the specified ambient temperature of 27°Cis the lowest available environment temperature, the reversible work determinedabove also represents the exergy, which is the maximum work potentialof the sensible energy contained in the iron block.