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Thermodynamics The useful work is the difference between these two:
Wu W Wsurr 2.43 1 1.43 kJ That is, 1.43 kJ of the work done is available for creating a useful effect such as rotating a shaft. Also, the heat transfer from the furnace to the system is determined from an energy balance on the system to be
E in E out¬ ¬ ¢E system ⎫ ⎪ ⎬ ⎪ ⎭
⎫ ⎪ ⎬ ⎪ ⎭
Net energy transfer by heat, work, and mass
Change in internal, kinetic, potential, etc., energies
Q in Wb,out ¢U mcV ¢T
Q
0
0
Q in Wb,out 2.43 kJ (b) The exergy destroyed during a process can be determined from an exergy balance, or directly from Xdestroyed T0Sgen. We will use the second approach since it is usually easier. But first we determine the entropy generation by applying an entropy balance on an extended system (system + immediate surroundings), which includes the temperature gradient zone between the cylinder and the furnace so that the temperature at the boundary where heat transfer occurs is TR 1200 K. This way, the entropy generation associated with the heat transfer is included. Also, the entropy change of the argon gas can be determined from Q /Tsys since its temperature remains constant.
S in S out¬
S gen ¢S system
⎫ ⎪ ⎬ ⎪ ⎭
⎫ ⎬ ⎭
⎫ ⎪ ⎬ ⎪ ⎭
Net entropy transfer by heat and mass
Entropy generation
Change in entropy
Q Q S gen ¢S system TR Tsys Therefore,
Sgen
Q Q 2.43 kJ 2.43 kJ 0.00405 kJ Tsys TR 400 K 1200 K
and
X destroyed T0 S gen 1300 K2 10.00405 kJ>K2 1.22 kJ/K (c) The reversible work, which represents the maximum useful work that could be produced Wrev,out, can be determined from the exergy balance by setting the exergy destruction equal to zero,
0 (reversible) X in X out X destroyed ¡ ¢X system
⎫ ⎪ ⎬ ⎪ ⎭
⎫ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎭
⎫ ⎪ ⎬ ⎪ ⎭
a1
Net exergy transfer by heat, work, and mass
Exergy destruction
Change in exergy
T0 b Q Wrev,out X 2 X 1 Tb
1U2 U1 2 P0 1V2 V1 2 T0 1S 2 S 1 2 0 Wsurr T0
Q Tsys