Environmental Engineering Reference
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and
γ
1
γ
1
=
V
V
P
P
γ
1
2
,
(5.15)
2
1
where γ  =  C p / C v is the specific heat ratio, and C p and C v are the specific
heats of hydrogen. For an ideal hydrogen gas, γ  = 1.4. The work W Q done
in the adiabatic process is
γ
1
γ
P
P
γ
2
W
Q =
nRT
1
.
(5.16)
1
γ
1
1
Usually, the compression process is carried out under several stages, and
the total work required for an l l-stage process is
γ
1
γ
P
P
l
γ
i
+
1
W
=
nRT
1
.
(5.17)
Q
1
γ
1
i
=
1
i
Multiple stage compression could significantly reduce the required energy.
For example, for a two-stage compression, if the initial and final pressures
are fixed at P 1 and P 2 , when the intermediate pressure P
i =
PP
1 2 , Equation
(5.17) gives the minimum work required,
γ
1
2
γ
P
P
2
γ
2
W
Q =
nRT
1
.
(5.18)
1
γ
1
1
If 1 mole of hydrogen is compressed from 1 atm at 20°C, Figure 5.4 shows
the comparison of the works W Q required for a one-stage and a two-stage
compression as a function of the final pressure P 2 . To compress the hydrogen
to 70 MPa, the two-stage process only requires ∼56% of energy of the one-
stage process. The higher the final pressure, the more the energy saved.
Similarly, a three-stage process, with intermediate pressure
γ
1
3
γ
P
P
3
γ
2 3
/
1 3
/
1 3
/
2 3
/
2
P
=
P P
,
P
=
P P
and
W
=
nRT
1 ,
i
1
1
2
i
2
1
2
Q
1
γ
1
1
can further reduce the required work (Fig. 5.4). Thus, with the increase of
number of compression stages, the required energy is reduced. But no sig-
nificant energy efficiency gain is expected when l  > 3.
When the pressure becomes higher, the behavior of hydrogen gas deviates
from that of an ideal gas, and the compression process can be better

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