1 Vernier scale
2 Fixed scale
3 Grease nipple
4 Threaded bush
5 Handwheel
6 Base
7 Frame
8 Threaded axle with piston
9 Piston cover
10 Outlet for thermal medium
11 Inlet for thermal medium
12 End plate
13 Cylinder
14 Conical seal
On delivery, the critical point apparatus is filled with
hydraulic fluid. The test gas is not included.
Before filling with the test gas, carry out a volume
calibration, as described in chapter 6, using air as an
approximation of an ideal gas.
Filling with the test gas is described in chapter 7.
Experimental investigations are described in chap-
ter 8.
Important notes on storage of the test gas and
equipment (if not in use for a long period) are stated
in chapter 9.
151614
1213
911
1. Contents of instruction manual
Owing to the inevitable diffusion of the test gas
through the conical seal, it is necessary to degas the
hydraulic fluid in the equipment, as described in
chapter 10. This must be done before the equipment
is put away for storage (after removing the test gas) or
if it has been in use for a long time.
The threaded bush in the frame must be lubricated
regularly and also inspected at lengthier intervals.
Refer to section 11 for instructions.
Maintenance work as described in chapter 12 is only
required if the rubber components get worn out and
their functionality is adversely affected.
1
2. Safety instructions
When used properly, the operation of the critical
point apparatus is not dangerous, since both the
experimenter and the equipment are protected by a
safety valve. However, it is extremely important to
observe a few precautionary measures:
• Read the instruction sheet thoroughly and follow
the instructions therein.
• Do not exceed the maximum permissible values
for pressure and temperature (60 bar and 1060°C).
• Do not operate the equipment without qualified
supervision.
• Always wear safety goggles.
Only increase the temperature at low pressure with
pure gas phase in the measuring cell.
• Before increasing the temperature, wind the
handwheel outwards so that maximum volume is
attained in the measuring cell.
When conducting adjustments, make sure that the
safety valve does not point in the direction of people
who could be injured or objects that could be damaged if the valve cover shoots out. When conducting
experiments, pay special attention too to the alignment of the safety valve.
• When setting up the apparatus, make sure that
the safety valve does not point in the direction of
people who could be injured or objects that could
be damaged.
• When adjusting the safety valve, wrap your arms
around the apparatus to reach the valve at the
back.
If the conical seal is overtaxed, it could get damaged
or even destroyed.
• Never set a pressure above 5 bar if the regulating
valve or the flush valve is open, i.e. if there is no
back pressure from the gas in the measuring cell.
• Never create underpressure by turning the hand
wheel inwards when the valves are shut.
In the frame there is a threaded bush, which is to be
regarded as a safety-related feature (see section 9).
• Lubricate the threaded bush every 100 cycles.
• Inspect the threaded bush annually.
To prevent damage by corrosion inside the instrument,
• use a 2:1 mixture of water and anti-freeze fluid as
the thermal medium.
Only as real gas for SF
and nitrogen as ideal gas.
6
3. Description
The critical point apparatus allows us to investigate
the compressibility and liquefaction of a gas. Measurements allow determination of the critical point for
the gas as well as the recording of isotherms for an
adiabatic p-V diagram (Clapeyron diagram). The gas
used for testing is sulphur hexafluoride (SF
). SF6 has a
6
critical temperature of 318.6°K (45.5°C) and a critical
pressure of 3.76 MPa (37.6 bar) which makes for a
simple experiment set-up.
The critical point apparatus consists of a transparent
measuring cell of particularly well sealed, pressureresistant design. The volume of the measuring cell
can be modified by turning a fine-adjustment wheel
and can be read by means of a fixed scale and a rotating vernier scale to an accuracy of one thousandth of
the maximum volume. The pressure is applied via a
hydraulic system using castor oil approved for medicinal use. The measuring cell and hydraulic system
are isolated from one another by a conical seal which
rolls up when there is an increase in pressure. This
design means that any pressure difference between
the measuring cell and the oil reservoir is negligible
in practical terms. A manometer measures not the
pressure of the actual gas but that of the oil, thus
eliminating any need for a space within the measuring cell. When observing transitions from gas to liquid
or vice versa, the lack of such a dead space means
that the development of the very first drop of liquid
as well as the disappearance of the last bubble of gas
can be observed. The measuring cell is surrounded by
a transparent chamber of water. A circulating thermostat arrangement (water bath) means that a constant
temperature can be maintained during the experiment with a high degree of accuracy. The temperature can be read and monitored using a thermometer.
The fact that volume, pressure and temperature can
all be read with a high degree of accuracy means that
accurate p-V diagrams or pV-p diagrams can be recorded without much difficulty. Pressure and temperature-dependent volume correction enable us to
achieve accurate quantitative results which are well in
agreement with published values.
4. Contents
1 Critical point apparatus, filled with hydraulic fluid
(castor oil). With attached gas connection fittings
for MINICAN® gas container and protection for gas
supply connections. Test gas (SF
) not included.
6
1 Oil filling device
1 Allen key, 1.3 mm (for grub screw on the vernier
thermal medium: mixture of water and anti freeze in the ratio 2:1
Determination of volume:
Piston diameter: 20.0 mm
Piston surface: 3.14 cm
Displaced volume: 3.14 cm
Maximum volume: 15.7 cm
2
2
× displacement
3
Scale division for
displacement: 0.05 mm
Maximum displacement: 50 mm
Determination of pressure:
Manometer: Class 1.0 (max. 1% deviation
from full scale value)
Measured quantity: Excess pressure
Indicator: 60 bar max.
Manometer diameter: 160 mm
Connections:
Hole for
temperature sensor: 6 mm dia.
Connections for
thermal medium: 7 mm dia.
Connection for
regulating valve: 1/8’’ dia.
Gas connection: 1/8’’ (3.17 mm) dia. (as
supplied)
General specifications:
Dimensions: 380 x 200 x 400 mm
3
Weight: 7 kg approx.
6. Volume calibration
6.1 Preliminary notes:
NOPM
Q
L
K
R
S
A
BCEF
Fig. 1: Cross-section of apparatus with measuring cell (A),
conical seal (B), oil chamber (C), piston (D), cylinder (E), heat casing (F), silicone seal (G), end
plate (H), square grommet (I), piston cover (J),
threaded axle (K), gasket (L), manometer connection (M), guide tube (N), spring (O), sleeve (P), hole
for temperature sensor (Q), circular grommet (R) and
valve plate (S)
D
I
H
G
One turn of the handwheel winds the piston into/out
of the cylinder by means of a threaded axle. This
leads to a change of volume in the oil chamber (see
Fig. 1). Since oil is practically incompressible and all
the other components other than the conical seal are
almost rigid, a change in volume in the oil chamber
causes the conical seal to deform, thereby creating an
almost equal change in volume ΔV
cell. As a first approximation for ΔV
sAV
G
where
(1)
2
cm143.A= and Δs = displacement of piston.
in the measuring
G
, we can assume:
G
The piston displacement is shown in divisions of
2 mm on the fixed scale. Intermediate values are read
on the vernier scale in divisions of 0.05 mm.
The fixed scale can be moved by loosening the two
knurled screws. The vernier scale can be repositioned
and turned around the threaded axle on loosening
the grub screw (between scale positions 0 9 and 1 0).
6.2 Zero point calibration:
The zero point for the volume scale must be determined by conducting a calibration.
For this, we take advantage of the fact that in a pressure range of 1-50 bar and in a temperature range of
270-340 K, air acts as a near-ideal gas (the real gas
factor has a deviation of less than 1% from 1). Therefore, at a constant temperature (e.g. room temperature) for two piston displacements s
and s1 and for
0
3
the corresponding pressures p0 and p1 of the trapped
T
⋅
⋅
=
air, we get:
spsp⋅=⋅ (2)
1100
Substituting
p
sΔ⋅
1
0
=
pp
−
s
01
sssΔ+=
10
and rearranging gives:
(3)
Rough calibration of scales:
• Open the regulating valve wide.
• Loosen the grub screw for the vernier scale by
half a turn (it is now possible to turn the scale
easily on the threaded axle without moving the
handwheel, although a counterpressure acts
against this independent movement).
• Wind the handwheel out till you detect a notice-
able resistance.
• Without turning the handwheel, turn the vernier
scale on the threaded axle till the 0.0 mark is on
the top and the fixed scale shows approx. 48 mm.
• Loosen the knurled screws of the fixed scale and
shift the scale to the side till the 48-mm bar is exactly above the centre line of the vernier scale
(see Fig. 2).
• Tighten the knurled screws again. In doing so,
make sure that the fixed scale does not press
against the vernier scale.
10020304050mm
00
19
18
17
•Calculate the zero corrected piston position s
1, corr
using Equation 3.
• Adjust the vernier scale to the corrected value
and, if necessary, move the scale again.
• If required, wind the handwheel out a little and
secure the vernier scale with the grub screw.
Measurement example:
= 1 bar, p1 = 16 bar, p1 – p0 = 15 bar
p
0
s
= 48.0 mm, s1 = 3.5 mm, Δs = 44.5 mm
0
Therefore,
s
= 2.97 mm.
1, corr
The vernier scale must therefore be adjusted so that
now only 2.97 mm are shown instead of 3.50 mm.
Note:
After calibrating the zero point, it is possible to obtain
qualitatively accurate measured values. With regard
to temperature
T and pressure p, it is also possible to
obtain quantitatively accurate measurements of the
isotherms in range around to the critical point where
the two phases exist simultaneously. However, especially in the liquid phase, the measured isotherms are
rather too widely separated.
6.3 Detailed calibration:
The exact relation between the volume VG in the
measuring cell and the scale reading
s is dependent
on the volume of oil in the oil chamber. The oil
chamber also expands marginally in proportion to the
pressure as a result of the spring in the manometer
tube. Additionally, when the temperature is increased, the castor oil expands to a greater extent
than the rest of the equipment. This means that the
pressure rises at a slightly greater rate at higher temperatures. All of these phenomena can be calculated
if appropriate calibration has been effected using air
as an ideal gas.
The ideal gas equation would thus be:
Vp
Rn
(4)
⋅=
16
with
J
3148.R =
molK
Fig. 2: Piston position reading at 48.0 mm
Zero correction:
• Shut the regulating valve (the pressure in the
measuring cell now corresponds to the ambient
pressure
p
= 1 bar. To within the accuracy of the
0
measurement, the manometer should display an
excess pressure of 0 bar).
• Wind the handwheel in till an excess pressure of
15 bar has been reached (absolute pressure
p
= 16 bar).
1
• Read the piston position s
displacement
Δs = s
– s1.
0
and calculate the
1
After taking the overpressure reading
pressure can be calculated from:
p = p
+ 1 bar (6)
e
The absolute temperature is given by:
T = ϑ + ϑ
where ϑ0 = 273.15°C (7)
0
The volume is given by:
sAV
G
where
(8)
2
cm143,A= and s is the “effective” piston
displacement.
From the measured displacement
p
, the absolute
e
s
, it is possible to
e
calculate the effective piston displacement as follows:
4
(9)
(
)
ϑ⋅−⋅++=
CpCsss
ϑ
pe0
By substituting in equation 4, we get:
⋅ϑ⋅β−⋅β++⋅
0
pe
ϑ+ϑ
0
Apssp
ϑ
(10)
0
=⋅−
Rn
If we take several readings at various temperatures
and pressures, we can calculate the term:
n
()
⎛
⎜
Q
=
∑
⎜
=
1i
⎝
p
ϑ+ϑ
0
Apssp
⋅ϑ⋅β−⋅β++⋅
ϑ
ii0ii
2
⎞
⎟
Rn
(11)
⋅−
⎟
⎠
Sample measurements:
Table 1: Measured values for calibration
i s
/ mm
e
ϑ
p / bar
1 40.0 20.0°C 6.6
2 20.0 20.0°C 12.4
3 10.0 20.0°C 23.3
4 5.0 20.0°C 41.8
5 3.5 20.0°C 53.9
The free parameters s
, βP, βϑ and n should be appro-
0
priately selected so that the value of Q is reduced to a
minimum.
Additionally required (see also chapter 8):
1 Compressor or bicycle pump and valve
1 Bath/circulating thermostat 1008653/1008654
1 Dig. quick-response pocket thermometer 1002803
1 Type K NiCr-Ni immersion sensor, -65°C-550°C
1002804
2 Silicone tubes, 1 m 1002622
1 l Anti-freeze fluid with corrosion-inhibiting additive
for aluminium engines (e.g., Glysantin® G30 ma-
nufactured by BASF)
Conducting the calibration:
• Connect the circulation thermostat as described
in chapter 8 and fill it with the water/anti-freeze
mixture.
• Connect the plastic tube (3-mm internal diameter)
to the 1/8" gas connection fittings.
• Open the regulating valve.
• Wind the handwheel outwards, making the piston
move till it reaches say the 46.0 mm position.
• Use a compressor or a bicycle pump to create an
excess air pressure of approx. 3-8 bar in the
measuring cell.
• Shut the regulating valve.
• To record measurements, vary the volume in the
measuring cell or the temperature of the thermostat and wait till a stationary equilibrium has
been attained. Then take a pressure reading.
• Use appropriate adjustment software to set the s
β
, βϑ and n parameters so that the quadratic
P
,
0
equation for the errors Q is reduced to a minimum (see equation 11).
• If you like, you can adjust the vernier scale
around s
so that this correction is not necessary.
0
With the set parameters, it is possible to calculate the
“effective” piston displacement s from the measured
displacement s
using Equation 9 and then to calcu-
e
late the calibrated measuring cell volume using Equation 8.
6 5.0 20.0°C 41.8
7 5.0 10.0°C 38.9
8 5.0 30.0°C 45.3
9 5.0 40.0°C 49.0
10 5.0 50.0°C 53.5
The following parameter values are obtained:
s
= 0.19 mm,
0
P
mm
0230
.=β
bar
n = 0.00288 mol.
7. Filling with test gas
7.1 Handling of sulphur hexafluoride:
Sulphur hexafluoride (SF6) is a non-toxic gas and is
absolutely safe for humans. The MAC value for danger
of suffocation on account of oxygen deprivation is
1000 ppm. That is equivalent to 6 filled measuring
cells per 1 m
However, SF
3
of air.
is extremely harmful to the environment
6
and can give rise to a greenhouse effect 24,000 times
stronger than CO
. Therefore, do not allow large quan-
2
tities to be released into the environment.
7.2 Gas connection via fixed pipes:
Additionally required:
1 SF
gas cylinder with manufacturer’s/supplier’s rec-
6
ommended gas fittings/valves, e.g. SH ILB gas cylinder
and Y11 L215DLB180 regulating valve from Airgas
(www.airgas.com).
1 Pipes with outer diameter of 1/8" and, if necessary,
adapters, e.g. from Swagelok (www.swagelok.com).
According to the principles of “good laboratory practice”, it is recommended to utilise a gas supply via
fixed pipes, especially if the equipment is regularly in
operation.
Filling begins with several flush cycles in which the air
is flushed out of the pipe. The number of cycles required to flush out the air depends on the length of
mm
,
0340.=β
ϑ
grd
and
5
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