8-134
8-181 Air is compressed in a piston-cylinder device. It is to be determined if this process is possible.
Assumptions 1 Changes in the kinetic and potential energies are negligible. 4 Air is an ideal gas with
constant specific heats. 3 The compression process is reversible.
Properties The properties of air at room temperature are R = 0.287 kPa˜m3/kg˜K, cp = 1.005 kJ/kg˜K (Table
A-2a).
Analysis We take the contents of the cylinder as the system. This is a closed system since no mass enters or
leaves. The energy balance for this stationary closed system can be expressed as
E in E out
'E system
Net energy transfer
by heat, work, and mass
Change in internal, kinetic,
potential, etc. energies
Wb,in Qout
'U
Wb,in Qout
mc p (T2 T1 )
Wb,in Qout
0
Qout
m(u 2 u1 )
(since T2
Air
100 kPa
27°C
T1 )
Wb,in
Heat
The work input for this isothermal, reversible process is
win
RT ln
P2
P1
q out
win
78.89 kJ/kg
(0.287 kJ/kg ˜ K)(300 K)ln
250 kPa
100 kPa
78.89 kJ/kg
That is,
The entropy change of air during this isothermal process is
's air
c p ln
T2
P
R ln 2
T1
P1
R ln
P2
P1
(0.287 kJ/kg ˜ K)ln
250 kPa
100 kPa
0.2630 kJ/kg ˜ K
The entropy change of the reservoir is
's R
qR
TR
78.89 kJ/kg
300 K
0.2630 kJ/kg ˜ K
Note that the sign of heat transfer is taken with respect to the reservoir. The total entropy change (i.e.,
entropy generation) is the sum of the entropy changes of air and the reservoir:
's total
's air 's R
0.2630 0.2630
0 kJ/kg ˜ K
Not only this process is possible but also completely reversible.
PROPRIETARY MATERIAL. © 2008 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and
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