under extreme high pressure or extreme low temperature are often corrected on the
basis of ideal gas. The real gas takes into account the microscopic theory of material
structure, such as the volume of gas molecule itself and the interaction force
between gas molecules, which can better reflect the objective reality.
The state equation for an ideal gas is
pV ¼
m
M
RT
ð8:49Þ
where
p Gas pressure Pa
ð Þ;
V Gas volume m
3
ð Þ;
m Gas mass kg
ð Þ;
M Gas molar mass kg=mol
ð
Þ ;
R Molar gas constant R ¼ 8:31J= mol K
ð
Þ;
T Gas thermodynamic temperature K
ð Þ.
The Van der Waals equation for real gases is
p þ
m
2
M 2
a
V 2
V À
m
M
b
¼
m
M
RT
ð8:50Þ
where
a Proportional coefficient m
6 Pa
À
Á =mol
2
Â
Ã
;
b Gas constant m
3
=mol
ð
Þ .
Among them, a and b are determined by measuring the pressure p k , volume V k ,
and temperature T k at the critical inflection point of gas, liquid, and solid
three-phase isotherms. There are
a ¼ 3V
2
k p k ¼
9
8
V c RT c ; b ¼
V k
3
ð8:51Þ
V k ¼
3
8
RT k
p k
ð8:52Þ
For dry air, there is T k ¼ À140:7
C; p k ¼ 3:72 MPa. The Van der Waals constants of several gases are shown in Table 8.5.
8.3.3 Inflation Mass of High-Pressure Gas Cylinders
For a certain volume of chamber, such as the chamber of hydraulic accumulator or
the cylinder of gas booster tank, it is usually pre-inflated at a certain temperature on
42
8 Pneumatic Actuators, Driving Elements and Accessories