464 | Thermodynamics
Assumptions 1 Air is an ideal gas. 2 The kinetic and potential energies are
negligible. 3 The properties of air at the inlet remain constant during the
entire charging process.
Analysis We take the rigid tank combined with the compressoras the sys-
tem. This is a control volumesince mass crosses the system boundary during
the process. We note that this is an unsteady-flow process since the mass
content of the system changes as the tank is charged. Also, there is only one
inlet and no exit.
The minimum work required for a process is the reversible work,which
can be determined from the exergy balance applied on the extended system
(system immediate surroundings) whose boundary is at the environment
temperature of T 0 (so that there is no exergy transfer accompanying heat
transfer to or from the environment) and by setting the exergy destruction
term equal to zero,Net exergy transfer Exergy Change
by heat, work, and mass destruction in exergyNote that f 1 c 1 0 since the initial air in the tank and the air entering
are at the state of the environment, and the exergy of a substance at the
state of the environment is zero. The final mass of air and the exergy of the
pressurized air in the tank at the end of the process areWe note thatTherefore,120.76 kJ>kg1 0.287 kJ>kg#K 21 300 K2aln
1000 kPa
100 kPa100 kPa
1000 kPa 1 bf 2 RT 0 aP 0
P 2 1 b RT 0 ln¬P 2
P 0RT 0 aln¬P 2
P 0P 0
P 2 1 bT 01 s 2 s 02 T 0 acp ln¬T 2
T 0Q0
R ln¬P 2
P 0bRT 0 ln¬P 2
P 0¬¬ 1 since T 2 T 02
P 01 v 2 v 02 P 0 aRT 2
P 2RT 0
P 0bRT 0 aP 0
P 21 b¬¬ 1 since T 2 T 02
P 01 v 2 v 02 T 01 s 2 s 02f 2 1 u 2 u 02 Q01 since T 2 T 02
P 01 v 2 v 02 T 01 s 2 s 02 V^22
2Q^0
gz 2 Q0m 2 P 2 V
RT 21 1000 kPa 21 200 m^32
1 0.287 kPa#m^3 >kg#K 21 300 K 22323 kgWrev,inm 2 f 2Wrev,inm 1 c 1 Q0
m 2 f 2 m 1 f 1 Q0XinXoutX 2 X 1X⎭in⎪⎬⎪X⎫out¬ (^) ⎭X⎪destroyed⎪⎪ (^) ⎬⎪⎪⎪⎫ ¢⎭⎪X⎬system⎪⎫
S^0 (reversible)