Second Year Laboratory
Variation of the Vapour Pressure of Liquid
Nitrogen with Temperature
G9
______________________________________________________________
Health and Safety Instructions.
This experiment uses liquid nitrogen, which, if incorrectly handled, can cause serious
burning, particularly to the eyes and skin. It is essential to observe the following safety
precautions:
•
Use protective gloves whenever pouring the liquid.
•
Wear the protective goggles provided whenever handling the liquid.
•
Read the notice adjacent to the equipment before beginning the experiment.
___________________________________________________________________________
16-10-06
Department of Physics and Astronomy, University of Sheffield
Second Year Laboratory
1. Aims
The aim of the experiment is to measure the vapour pressure of liquid nitrogen in an
experiment, which depends on the careful control of vacuum conditions and the calibration of
temperature.
2. Apparatus
•
Stainless steel Dewar for liquid nitrogen mounted into the bench,
•
pumping lines with diaphragm and needle valves,
•
rotary vacuum pump,
•
digital manometer,
•
Bourden pressure gauge
•
digital thermometer.
3. Background
It is well known that if the pressure of a gas above a liquid is reduced, the liquid will
evaporate to fill the partial vacuum created. The latent heat of evaporation must come from
the liquid itself and this causes the temperature of the liquid to fall. This effect is exploited in
low temperature physics to obtain temperatures below the normal boiling point of liquid
helium, 4.2K, by pumping on the vapour above its surface.
A liquid boiling into a gas is an example of a first order phase change, which is characterised
by a change in the specific volume between the two phases, accompanied by a latent heat.
P
s
l
B
A
g
T
Figure 1. The P,T phase diagram of a material
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Department of Physics and Astronomy, University of Sheffield
Second Year Laboratory
The (P,T) phase diagram of a material is given in Figure 1, showing the extent of the solid
(s), liquid (l) and gaseous (g) states.
At the point A on the phase diagram shown in figure 1, the Gibbs Function per unit mass
obeys the equation
Gg(T, P)=Gl(T, P)
(1)
where the subscripts g and l refer to the gas and liquid phases respectively.
At the neighbouring point B,
Gg(T+dT, P+dP)=Gl(T+dT, P+dP).
(2)
Equation 2 can be expanded by Taylor’s theorem to give
 ∂G g 
 ∂G g 
 ∂G 
 ∂G 
G g (T, P) + 
 dT + 
 dP = Gl (T, P) +  l  dT +  l  dP
 ∂T  P
 ∂P  T
 ∂T  P
 ∂P  T
 ∂G g 
 ∂G 
 ∂G g  
 ∂G  
 −  l  dT =  l  − 
 dP ,

 ∂T  P  ∂T  P 
 ∂P  T  ∂P  T 
and since,
 ∂G 
V = 
 ∂P  T
 ∂G 
S = −
 ,
 ∂T  P
this gives,
(S
g
)
(
)
− S l dT = V g − Vl dP ,
so,
dP Sg − Sl
.
=
dT Vg − Vl
(3)
If a phase change occurs in a system with a corresponding change in entropy, there will be a
transfer of heat to or from the surroundings. This is the latent heat L. If a fixed mass changes
from a liquid to the vapour, at the temperature T, then,
(
)
L = T Sg − Sl .
(4)
If Sg > Sl, then L is positive and heat has to be supplied to the system. So substituting into
Equation 3 gives,
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Department of Physics and Astronomy, University of Sheffield
dP
L
=
dT T Vg − Vl
(
Second Year Laboratory
)
If the volume of liquid is neglected in relation to the volume of the gas formed, and we
assume that the gas obeys the perfect gas law,
PV=RT
where V is the volume of one mole and R is the gas constant, then
dP LP
=
dT RT 2
Hence if L is a constant
dP L dT
=
P
R T2
ln( P ) = −
L
+ const.
RT
(5)
The procedure for determining L, the Latent Heat per mole is given below, but from the
equation you can see that the experiment consists of measuring the temperature T of the
liquid nitrogen as a function of the pressure P which is created over the liquid surface by
pumping.
4. Experiment
The keys to successful execution of this experiment are precise control of the pumping
rate and accurate physical manipulation of the valves in the pumping lines. It will also
be necessary to decide whether the experiment has been performed under stabilised
conditions or not. It is envisaged that the experiment may need to be performed two, three or
more times.
•
The first run should give some indication of the magnitude of the temperature
changes, which are produced as a function of the pressure. It may not yield many
useful data points!
•
The second run will provide data which should be analysed fully to determine a value
for the Latent Heat of liquid nitrogen
•
The third (and any subsequent) runs should be performed to improve on the value for
the Latent Heat of liquid nitrogen and to ensure that the experimental conditions were
indeed satisfied.
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Department of Physics and Astronomy, University of Sheffield
Second Year Laboratory
The following describes how to carry out one complete run.
1. Despite the manufacturer’s specifications the calibration of the digital thermometers
used in this experiment has not been found to be very reliable at low temperatures.
Make a three-point calibration of the thermometer using iced water, dry ice and liquid
nitrogen and use the corrected temperatures in all the subsequent analysis. Obtain the
calibration curve by performing a χ2 fit to the data. Do not forget that most of the data
points recorded in this experiment will be below the temperature of liquid nitrogen.
The calibration curve must therefore be extended downwards from the lowest data
point.
2. Confirm the calibration of the digital manometer. Ensure that the rubber O-ring seal
in the lid of the Dewar is completely free from any dirt. Seal the Dewar with the lid.
Open the diaphragm valve (large and silver) fully and evacuate using the vacuum
pump to the lowest pressure the pump allows, which will correspond to one
atmosphere on the Bourden gauge. Measure the pressure using the digital manometer
and compare directly with the value given in Kaye and Laby.
Note: The digital manometer can display the pressure on a number of different scales.
The kilopascal (kPa) scale is the most suitable. Atmospheric pressure is 101.3kPa.
Note that the pressures measured will be from 101.3kPa downwards although the
digital manometer displays atmospheric pressure as zero. In the calculation it is
necessary to use an adjusted pressure scale,
Actual pressure value = 101.3kPa + the indicated (-ve) pressure value.
(e.g. 11.6kPa = 101.3kPa – 89.7kPa indicated)
3. Make sure the Dewar is dry inside then fill it about one third full with liquid nitrogen
observing the precautions on page 1. Do not let the liquid nitrogen fall on the rubber
O-ring and freeze it as it will not then make a vacuum seal.
4. Measure the temperature at atmospheric pressure using the digital thermometer.
5. After making measurements at atmospheric pressure the pressure of the vapour can
reduced to a lower level by pumping with the rotary pump. The pressure is controlled
by use of the needle valve and diaphragm valve. The diaphragm valve (large and
silver) is used to make coarse adjustments and the needle valve (small and
black/silver) is used to make fine adjustments.
i.
Turn the pump on.
ii.
Before opening the diaphragm valve make sure that the needle valve is open
(turn anticlockwise). This is to ensure that when the diaphragm valve is
closed a ‘back’ pressure is not created thus causing the pressure to drop
sharply. Next open the diaphragm valve (anticlockwise). It is good idea to
increase the vacuum slowly.
iii.
When the pressure has reached the desired level slowly close the diaphragm
valve. The pressure will now drop slightly but should soon start to rise. To
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Department of Physics and Astronomy, University of Sheffield
Second Year Laboratory
counteract this the needle valve must be gradually closed until the pressure
remains constant. When closing the valve always stop as soon as it gets
slightly harder to twist. The fact that the pressure is dropping is just due to
vapour from the nitrogen. The needle valve is delicate and trying to force it
shut will damage it.
Note 1: It is important to remember that a balance between the stimulated evaporation
from the nitrogen and the partial vacuum created over its surface is required in this
experiment. If the pressure is dropping then the needle valve is closed too much. If the
pressure is rising then the needle valve is open too much (or the diaphragm valve is
still open).
Note 2: Pumping with the diaphragm valve fully open for any significant length of
time can depress the temperature in the Dewar enough to solidify the nitrogen. In this
case, it is no longer in a regime where the Latent Heat of liquid nitrogen can be
determined, but more importantly, it will be impossible to take the lid off the Dewar,
if the probes are frozen in!
6. Measure the temperature and vapour pressure using the digital thermometer and
digital manometer.
The thermal inertia of the probe of the digital thermometer is small but nevertheless it
will be necessary to stabilise the vapour pressure for a some time in order to get an
accurate measurement of the temperature.
7. Stabilise the pressure as described in step 5 at a number of other values down to as
low a pressure as you can conveniently achieve and measure the value of the
temperature reached at each pressure. Do not worry too much about trying to get
equally spaced data points but concentrate on making the observation when the
conditions are stable. It is important to remember that the boiling point (-195.80°C,
77.36K) and the melting point (-210.00°C, 63.16K) of nitrogen are quite close as
explained in Note 2 above.
8. In order to remove the lid of the Dewar it is necessary to turn the vacuum pump off at
the mains to automatically open its pressure relief valve. If the pump is turned off
using the switch on the pump itself, the vacuum inside the pumping system will be
retained.
Data Analysis
9. Plot a suitable graph from the results obtained from which the Latent Heat of
vaporisation of nitrogen, L, can be determined through the application of equation 5
above.
10. What is the value of L? How accurate is this value? Note that if equation 5 is plotted
using the accepted value of L, this may give some indication of where the results you
obtained depart from the idealised results.
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Department of Physics and Astronomy, University of Sheffield
Second Year Laboratory
11. How well does this compare to the literature value? If there are any discrepancies can
these be understood or interpreted by making comparison between the actual
experimental data and the simulated data obtained with the accepted value of L?
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