Thermodynamics

456 | ThermodynamicsThe useful work is the difference between these two:W u W W surr 2.43 1 1.43 kJThat is, 1.43 kJ of the work done is available for creating a useful effectsuch as rotating a shaft.Also, the heat transfer from the furnace to the system is determined froman energy balance on the system to beE in E out ¢E systemNet energy transferby heat, work, and massChange in internal, kinetic,potential, etc., energies⎫⎪⎬⎪⎭⎫⎪⎬⎪⎭⎫ ⎪⎬⎪⎭⎫⎬⎭⎫⎪⎬⎪⎭Q in W b,out ¢U mc V ¢T Q0 0Q in W b,out 2.43 kJ(b) The exergy destroyed during a process can be determined from an exergybalance, or directly from X destroyed T 0 S gen . We will use the second approachsince it is usually easier. But first we determine the entropy generation byapplying an entropy balance on an extended system (system + immediatesurroundings), which includes the temperature gradient zone between thecylinder and the furnace so that the temperature at the boundary where heattransfer occurs is T R 1200 K. This way, the entropy generation associatedwith the heat transfer is included. Also, the entropy change of the argon gascan be determined from Q/T sys since its temperature remains constant.S in S out S gen ¢S systemTherefore,Net entropy transfer Entropy Changeby heat and mass generation in entropyQ ST gen ¢S system QR T sysS gen Q Q 2.43 kJ 2.43 kJ 0.00405 kJT sys T R 400 K 1200 KandX destroyed T 0 S gen 1300 K2 10.00405 kJ>K2 1.22 kJ/K(c) The reversible work, which represents the maximum useful work thatcould be produced W rev,out , can be determined from the exergy balance bysetting the exergy destruction equal to zero,X in X out X destroyed ¡0 (reversible)Net exergy transfer Exergy Changeby heat, work, and mass destruction in exergy⎫ ⎪⎬⎪⎭⎫⎪⎬⎪⎭⎫⎪⎪⎪⎪⎬⎪⎪⎪⎪⎭a 1 T 0T bb Q W rev,out X 2 X 1 1U 2 U 1 2 P 0 1V 2 V 1 2 T 0 1S 2 S 1 2 0 W surr T 0 QT sys ¢X system