Lab 2
The Saturation Curve of H2O
04/23/2014
Ting Zhang– First Author, Abstract and Error Analysis
Kanchan Bhattacharyya – Discussion and Conclusion
Matthew Stevens – Introduction and Results
Xie Zheng – Lists of Equipment, Experimental Theory and Experiment
al Procedure
I. Abstract
This experiment consists of three parts. First of all, students are required to calibrate a
strain-gage pressure transducer. Then, students are asked to measure the saturation
pressure of H2O as a function of temperature. Finally, students are required to compare the
results to the international reference data. This experiment involved a lot of variables to be
measured such as resistance R and voltage V. The temperature of the system is measured by
using a resistance temperature thermometer(RTD), and the relationship of temperature T
and resistance R can be shown by using a calibrated equation. At the same time, the
pressure is measured using a strain gage, and it also has certain relationship with measured
voltage v. That is the reason why students can get experimental temperature T and
experimental pressure P by using measured variables R and V respectively.
II. Introduction
We all know from experience that substances can exist in one of three phases, and
that a substance may exist in one or more of these distinct phases. A glass of ice water
on a hot summer day for example, will contain not both the solid ice phase of water and
the liquid water phase existing simultaneously until the ice melts in the summer heat.
Similarly, we boil water for cooking using our kitchen stove, raising the temperature of
the liquid water to its boiling point at which it begins to evaporate into a
complementary gas phase. Even though we are exposed to these situations in our
every-day lives, we often forget their implications on the world around us. For example,
to say that water boils at a particular temperature is incorrect. The correct statement is,
water boils at a particular temperature at a particular pressure. That is, the temperature
at which water starts boiling depends on the pressure. [1]
At a given pressure, the temperature at which a pure substances changes phase is
called the saturation temperature and the pressure at which a pure substance changes
phase is called the saturation pressure. During a phase change-process, pressure and
temperature are dependent properties, and there is a definite relation between them. [1]
For example, we find that at sea-level where atmospheric pressure is 1 atmosphere
water will boil at 100°C while it will boil at about 95°C in elevated Denver Colorado
where the pressure is about 0.83 atm.
[2]
A plot of the saturation temperature versus the saturation pressure is called a
liquid-vapor saturation curve. All pure substances possess such a curve, which describes
how these saturation temperatures and pressures vary relative to one another.
In this
report we explore the variation of saturation pressure with temperature, and the results
will be compared to those reported by international reference data.
III. List of Equipment
IV. Experimental Theory
Theory
A phase diagram in physical chemistry, engineering, mineralogy, and materials
science is a type of chart used to show conditions at which thermodynamically
distinct phases can occur at equilibrium. In the temperature-pressure plane, the phase
diagram consists of curves that indicate the value of T and p for which the pure
substance separate into two or more phases. In this experiment, we are using water as
the specimen since water always plays an important role in the design of vapor power
systems and heating and cooling condenses. As for the purpose of this experiment, we
are going to locate the curve of water’s liquid-vapor saturation.
In this experiment, we are using an equation which is determined by an international
congress of scientists and engineers:
𝑝𝑠𝑎𝑡 (𝑇) =
−3.12740+11.6488𝑡−14.5672𝑡 2 +6.11868𝑡 3
1.0−2.35598𝑡+1.89103𝑡 2 −0.514442𝑡 3
for temperature range from 273.1K to 324K. Here,
(Eq.1)
t = T/300, and T has units of degrees
Kelvin.
In the experiment, the water will be keep in a glass bulb to make it present in both
liquid and vapor phases. The temperature of the bulb will be varied by using the bath which
could change the temperature according to setup. For measuring the psat,a platinum
resistance thermometer (RTD) will be used and the relation between resistance and
temperature is shown:
𝑇 = 1241.7221 + 261.1236𝑟 + 10.0059𝑟 2 + 0.7585𝑟 3
where
(Eq.2)
𝑟=
𝑅
112𝛺
As for the pressure, it is measured using a fou-arm strain gage resistance bridge
embedded in a silicon crystal that is mounted on a diaphragm. The output voltage is linearly
proportional to the excitation. Thus changes in the excitation voltage will cause the output
voltage to change even if the pressure is constant. The pressure is given by:
𝑝 = 𝑎 + 𝑏𝑉
(Eq.3)
where V is the bridge output voltage. The constant a and b will be determined from
two measurements of p and V usting both the pressure transducer and a reference pressure.
V. Experimental Procedure
Since the experiment was already setup in the lab, we check the connections of the
equipment and make sure we have all the instruments we need. First of all, we recorded the
readings shown on the multimeter and then set the temperature of the bath as 55 °C which took
a while to heat up the water in it. When the temperature of the water reached 55°C, we started
to record the readings for pressure and temperature for every 30 seconds. After doing the test
for 55°C, we turned off the bath to prevent it to be overheated.
After taking 10 trials, we were going to set the temperature of the bath as 45°C. We used the
equation to find out how much water needed to be replaced with cold water:
𝑇𝑖 − 𝑇𝑓
ℎ
=
𝐻
𝑇𝑖 − 𝑇𝑤
Where H is the original height of the water, h indicates the water that needed to be taken
out, Ti is the bath’s temperature, Tw is the room temperature and Tf is the temperature we need.
By doing the calculation with above equation, we knew how much water we needed to take
out and replaced with cold water by using the tube and tank. Then, we repeat the steps to do the
trials for 35°C, 28°C and 25°C.
Once we finished, we turned off the bath and meters, cleaned up the lab and put
everything back.
VI. Results
a. Plot a graph of Pressure vs. Temperature in Theory by using Equation 1
Governing Equation:
−3.12740 + 11.6488𝑡 − 14.5672𝑡 2 + 6.11868𝑡 3
𝑝𝑠𝑎𝑡 (𝑇) =
(1)
1.0 − 2.35598𝑡 + 1.89103𝑡 2 − 0.514442𝑡 3
Temperature, T (°C)
10.0000
11.0000
12.0000
13.0000
14.0000
15.0000
16.0000
17.0000
18.0000
19.0000
20.0000
21.0000
22.0000
23.0000
24.0000
Pressure, Psat (T) (kpa)
1.2241
1.3086
1.3982
1.4932
1.5938
1.7003
1.8130
1.9322
2.0582
2.1913
2.3320
2.4805
2.6371
2.8024
2.9766
25.0000
26.0000
27.0000
28.0000
29.0000
30.0000
31.0000
32.0000
33.0000
34.0000
35.0000
36.0000
37.0000
38.0000
39.0000
40.0000
3.1603
3.3537
3.5573
3.7717
3.9972
4.2343
4.4836
4.7456
5.0207
5.3095
5.6127
5.9307
6.2643
6.6139
6.9803
7.3640
Table1: This table shows 30 sets of temperatures and their corresponding pressures that are
calculated by using Equation 1 in order to get a smooth and continuous curve to represent
the relationship of temperature and pressure in theory.
Pressure vs. Temperature in Theory
Saturation Pressure, Psat (kPa)
25
20
15
10
5
0
25
30
35
40
45
50
55
60
65
Temperature T (°C)
Pressure vs. Temperature in theory
Fig1: This figure shows the relation between pressure and temperature that is calculated
from equation 1 in lab manual.
b. Plot five points of Measured Pressure vs. Measured Temperature and their
corresponding error bars
Mean Temperature
T (°C)
55.110
45.145
32.166
28.175
25.582
Mean Saturation Pressure
Psat (kpa)
15.807
9.640
4.790
3.810
3.275
Table2 : This table shows the measured mean temperatures and their corresponding
pressure(The procedures of calculating these values are showed in Appendix Section.)
Saturation Pressure, Psat (kPa)
Saturation Pressure vs. Temperature
18.00
T = 55°C
16.00
14.00
12.00
T = 45°C
10.00
8.00
6.00
T = 28°C
4.00
T = 32°C
T = 25°C
2.00
0.00
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
Temperature, T (°C)
Fig2: This figure shows the relations between measured pressure and measured
temperatures at T=55, 45, 32, 28 and 25 °C. The error bars in this plot is proportional
enlarged in order to let reader realize the existence of errors in both measured pressure and
measured temperature, due to the real errors for these five points are so many that error
bars in this plot can not be figured out by eyes. The real errors are shown in the following
table.
Tsat (°C)
55
45
32
28
25
Mean
Temperature, T (°C)
55.11
45.15
32.17
28.18
25.58
Temperature
error∆𝑇𝑡𝑜𝑡𝑎𝑙 (°C)
0
0.004
0
0.00058
0.825
Mean Saturation
Pressure, Psat(kpa)
15.81
9.64
4.79
3.81
3.28
Pressure error
∆𝑝𝑡𝑜𝑡𝑎𝑙 (kpa)
0
0.00050
0
2.82709*10-05
0.0351
Table 3: this table shows final results of the calculated uncertainties for ∆𝑇𝑡𝑜𝑡𝑎𝑙 and
∆p𝑡𝑜𝑡𝑎𝑙 at 55, 45, 32, 28 and 25 °C respectively. (The steps of calculating the errors are
illustrated in the Error Analysis Section.)
c. Compare the measured pressure and theoretical pressure.
Mean Temperaure,
T (°C)
55.11
45.15
32.17
28.18
25.58
Theoretical Saturation
Pressure, Psat(kpa)
15.81
9.64
4.79
3.81
3.28
Measured Saturation
Pressure P'(kpa)
15.44
9.29
4.53
3.47
2.86
ε(%)
-2.33
-3.64
-5.34
-8.95
-12.56
Table 4: this table shows final results of the calculated theoretical Pressure, measured
pressure and their relative error at 55.11, 45.15, 32.17, 28.18 and 25.58 °C respectively. (The
steps of calculating the errors are illustrated in the Error Analysis Section.)
Percent Error vs. Temperature in theory
Percent Error (%)
0.00
25.00
-2.00
30.00
35.00
40.00
45.00
50.00
55.00
60.00
-4.00
-6.00
-8.00
-10.00
-12.00
-14.00
Temperature T (°C)
Percent Error vs. Temperature in theory
Fig3: This figure shows the relations between percent of errors and measured temperatures.
d. Compare the measured values and theoretical values.
Saturaton Pressure, Psat (kPa)
Liquid Vapor Saturation Curve
25.0000
20.0000
15.0000
10.0000
5.0000
0.0000
0.0000
10.0000
20.0000
30.0000
40.0000
50.0000
60.0000
70.0000
Temperature, T (°C)
Calculated Pressure and Temperature from Eq.1
measured pressure and temperature
Fig4: This figure combines figure 1 and figure 2. As a result, we can see the measured values
perfectly fit the curve that is calculated from Equation 1.
VII. DISCUSSION
This experiment was designed firstly to measure saturation pressure using a calibrated
strain-gage pressure transducer which outputs a voltage for a given pressure according to
the linear equation in Eqn 3 (calibrated P as a function of V). This set of experimental values
for saturation pressures at the chosen temperatures can be compared to semi-empirical
values obtained from Eqn 1 (Psat (T) curve fit) which represents the international standard.
The high precision of the temperatures inputted into Eqn 1 (Psat (T) curve fit) come from an
RTD, whose resistive values can be converted to temperature in Celsius from Eqn 2 (RTD T in
terms of “r”).
In order to calibrate the pressure transducer, the bulb’s voltage reading at the start of
the experiment is used as one reference point, expected to correspond with the value of
atmospheric pressure. (Note that this was a particularly humid day when it had just rained,
so the atmospheric pressure was lower – however this was accounted for with a precise
reading of the exact pressure.) The second reference point is obtained when the bulb is
attached to a vacuum pump, which causes saturation pressures to drop to near zero and
result in voltage readings of around ~0.05 mV, which is accepted as a zero point. These two
points establish the pressure vs. voltage relationship needed for calibration in Eqn 3, and
obtain the experimental values of saturation pressure. The other measurements were taken
in incremental steps, where water in the tank was siphoned out in exchange for cooler tap
water, in fixed proportions such that the water bath would cool to the desired temperatures.
It is at these temperatures, that the RTD resistance reading was taken, later to be converted
to exact temperature using Eqn 2, which is then used for Eqn 1, to obtain the semi-empirical
(true) values of saturation pressure.
Examining Table 2-5, (NOTE: 2 tables are labeled Table “2” in excel spreadsheet; just
listing all temperature tables here 55,45,35,…) it can be seen that all values are very
consistent for all the data points across all trials, proved statistically in Table 6 (mean T, P,
stand. Dev), where the greatest variation was at the T = 25 C trial where the standard
deviation was 0.825848049 for temperature (which appears to be the outlier as the rest are
0.002039181 and below) and 0.035119828 for the saturation pressure. (where the rest were
0.000500866 and below)
Now, let’s examine the relationship between saturation pressure and temperature.
Listing data points from the first trial of each data set from Tables 2-5 for given temperatures
as (T, Psat (T), Psat (V)): At T = 55
℃ (55.11, 15.81, 15.4178426), T = 45
℃
(45.10435296, 9.62, 9.2641986), T = 32
℃ (32.16557033, 4.79, 4.6162552) T = 28
℃
(28.11687396, 3.80, 3.4887686), and at T = 25
℃ (25.26049921, 3.21, 2.857049). From
here it’s clear that with a drop in temperature, vapor pressure drops as well. To explain this
qualitatively, this results from the fact that at lower temperatures, the existing gaseous
water vapor molecules have less kinetic energy and eventually slowly condense back down
into the liquid state, hence resulting in lower partial pressures of water and lower saturation
pressures. The rate of water evaporating from the liquid surface also decreases for similar
reasons, resulting in an equilibrium with less exchange between the two mediums.
However, it is interesting to point out that the saturation pressures calculated from
the pressure-voltage relationship using the two-point calibration, were consistently lower by
about ~0.4 kPa at all temperatures compared to the international standard. The difference
doesn’t seem like a lot but the fact that it is consistently propagated deserves some
attention. This may be an adverse effect from the heavy rain on the day of the experiment
which is resulted in higher humidity and a significantly lower atmospheric pressure. However,
this is a bit counterintuitive given that that humidity is equivalent to higher saturation
pressures of water. Rather, the exact opposite is being observed. It is also true that the lower
atmospheric pressure is usually not the result of but the cause of rain as the lower pressure
provides atmospheric lift causing the air to rise and water particles to condense into clouds.
The high humidity is also simply an after-effect of this rain. A retest of this experiment under
dry conditions would be ideal to verify if this is purely an experimentally-based error which
is plausible given that the calibration has only 2 points, one of which is attributed as the zero
point, or if other humidity-based effects are playing a major role in this error.
Lastly, examining the liquid-vapor pressure curve, where the international standard
from Eqn 1 (Psat vs. T fit) is plotted as a smooth curve of 20+ data points and where the
experimental data at the five different temperatures are plotted as discrete points. These
two correlate extremely well, which is something we can verify from the tables we examined
above that actually tabulate the data for the two graphs. Since the temperatures for both
graphs were obtained from the RTD standard to a high precision, and the saturation
pressures observed in Columns 5 & 6 in Tables 2 – 5 are nearly the same with a consistent
~0.4 kPa difference throughout all measurements. This discrepancy correlates to about 2.6%
at T = 55 ℃ and is small, such that the experimental data points fit the international
standard curve extremely well.
VIII. Error Analysis
Part One: Calculate the uncertainties ∆𝑇𝑡𝑜𝑡𝑎𝑙
The total uncertainty consists of two parts, one is measurement uncertainty, the
other is instrumental uncertainty. In this experiment, the instrumental uncertainty is 0.01
degree centigrade, so we have to calculate measurement uncertainty In order to get the
total uncertainty value for ∆𝑇.
a) The uncertainty tree for ∆𝑇
Figure 5: This uncertainty tree illustrates steps of breaking down the calculation for
measurement uncertainty ∆𝑻 into tree parts. First of all, we need to calculate the
uncertainty for the measured resistance ∆𝑹, after that, we can calculate ∆𝒓. Finally we
can get measurement uncertainty ∆𝑻 after we have ∆𝑹
b) Calculate the uncertainties ∆𝑅
Use T=45 (°C) as an example.
Measurement, i
Resistance, R (kOhms)
1
2
117.89
117.93
3
117.93
4
117.93
5
6
117.91
117.9
7
8
117.9
117.89
9
117.89
10
117.89
average
117.906
Standard deviation
0.01776
t95
Sx
2.262
0.012703856
Table 5: This table shows the measurement data for resistance R and its mean value and
standard deviation value at T=45°C
The step of calculating ∆R at T=45°C is as follows.
∆R = t 𝑣,𝑝 ∗
𝑆𝑋
√𝑁
= 2.262 ∗
0.01776
√10
= 0.012703856
Example answer:
𝑅 = 117.906 ± 0.012703856(95%)
b) Calculate the uncertainties ∆𝑟
The relationship between 𝑟 and 𝑅 is as shown in the uncertainty tree above. From the
equation above, we can tell that r and R is linear, so the uncertainties for them should be
linear as well
∆𝑅
0.012703856
∆𝑟 =
=
= 0.000113427285638628
112
112
𝑟 = 1.0527 ± 0.00015857
c) Calculate the uncertainties ∆𝑇
Governing equation to calculate ∆𝑇:
∆𝑇 =
𝑑𝑇
∆𝑟 = (261.1236 + 2 ∗ 10.0059𝑟 + 3 ∗ 0.7585𝑟 2 ) ∗ ∆𝑟
𝑑𝑟
= (261.1236 + 2 ∗ 10.0059 ∗ (0.012703856) + 3
∗ 0.7585 ∗ (0.012703856)2 ) ∗ (0.00015857) = 0.0415
d) Calculate the total uncertainties ∆𝑇𝑡𝑜𝑡𝑎𝑙
Governing equation to calculate ∆𝑇𝑡𝑜𝑡𝑎𝑙 :
∆𝑇𝑡𝑜𝑡𝑎𝑙 = √∆𝑇 2 + ∆𝑇𝑖𝑛𝑠𝑡 2 = √(0.0415)2 + (0.01)2 = 0.0427
𝑇 = T𝑎𝑣𝑒𝑟𝑎𝑔𝑒 ± ∆T𝑡𝑜𝑡𝑎𝑙 = 45.15 ± 0.0427
Part Two: Calculate the uncertainties ∆𝑝𝑡𝑜𝑡𝑎𝑙
The total uncertainty consists of two parts, one is measurement uncertainty, the
other is instrumental uncertainty. In this experiment, the instrumental uncertainty is 0.5%
degree centigrade, so we have to calculate measurement uncertainty In order to get the
total uncertainty value for ∆𝑝.
a) The uncertainty tree for ∆𝑝
Figure 6: This uncertainty tree illustrates steps of breaking down the calculation for
measurement uncertainty ∆𝒑 into two parts. First of all, we need to calculate the
uncertainty for the measured resistance ∆𝒗, after that, we can calculate ∆𝒑.
b) Calculate the uncertainties ∆𝑣
Measurement, i
1
2
3
4
5
6
7
8
9
10
average
Standard deviation
t95
Sx
Voltage, V (mV)
9.563
9.616
9.615
9.61
9.594
9.583
9.579
9.574
9.571
9.57
9.5875
0.01992
2.262
0.01424892
Table 6: This table shows the measurement data for voltage v and its mean value and
standard deviation value at T=45°C
The step of calculating ∆v at T=45°C is as follows.
∆v = t 𝑣,𝑝 ∗
𝑆𝑋
√𝑁
= 2.262 ∗
0.01992
√10
= 0.01425
v at T=45°C is
𝑣 = 9.5875 ± 0.01425(95%)
b) Calculate the uncertainties ∆𝑝
𝑑𝑝
∆𝑝 =
∆𝑣 = 𝑏 ∗ (∆𝑣) = 1.0222 ∗ 0.01425 = 0.01457
𝑑𝑣
c) Calculate the uncertainties ∆𝑝𝑡𝑜𝑡𝑎𝑙
∆𝑝𝑡𝑜𝑡𝑎𝑙 = √∆𝑝2 + 𝑇𝑖𝑛𝑠𝑡 2 = √(0.01457)2 + (0.04820)2 = 0.0050
p at T=45°C is
𝑝 = p𝑎𝑣𝑒𝑟𝑎𝑔𝑒 ± ∆p𝑡𝑜𝑡𝑎𝑙 = 9.6402 ± 0.0050
Part three: show the results of calculated uncertainties for ∆𝑇𝑡𝑜𝑡𝑎𝑙 and ∆p𝑡𝑜𝑡𝑎𝑙 at different
temperatures
Tsat (°C)
55
45
32
28
25
Mean
Temperature, T (°C)
55.11
45.15
32.17
28.18
25.58
Temperature
error∆𝑇𝑡𝑜𝑡𝑎𝑙 (°C)
0
0.004
0
0.00058
0.825
Mean Saturation
Pressure, Psat(kpa)
15.81
9.64
4.79
3.81
3.28
Pressure error
∆𝑝𝑡𝑜𝑡𝑎𝑙 (kpa)
0
0.00050
0
2.82709*10-05
0.0351
Table 7: this table shows the calculated uncertainties for ∆𝑇𝑡𝑜𝑡𝑎𝑙 and ∆p𝑡𝑜𝑡𝑎𝑙 at 55, 45, 32,
28 and 25 °C respectively.
IX. CONCLUSION
The experiment’s main goal to measure pressure using a calibrated pressure-transducer
and test whether this vacuum-based method of calculating saturation pressures at varied
temperatures would yield results consistent with international standards. The first
qualitative result that we expected was to observe that pressure indeed drops with
temperature, which was explained by the lower molecular activity at a given temperature,
less exchange between the liquid and gaseous medium and lower vapor/saturation
pressures overall. As for comparing the two saturation pressures, the one predicted from
Eqn 1 which represents the best-fit curve of saturation pressure as a function of
temperature, and the experimental values from the pressure-voltage relation of Eqn 3 – they
correlate extremely well, with only a ~0.4 kPa difference. Where this difference comes from
is still inconclusive but given its remarkable consistency, it may be either an error resulting
from the initial calibration (which is entirely plausible given that only two data points, one of
which is the zero point were used) or truly from an adverse effect from the heavy rain on
that day. This can be easily tested by retrying the experiment on a day with dry weather and
close to normal high atmospheric pressures and seeing whether or not this error is still
pervasive in the measurements.
Aside from this consistent error, the experimental setup proves to be quite useful in this
application. One issue that arose in conducting this experiment was the shutdown of the
bath temperature sensor due to ‘overheating’ which requires tedious shutting off of the
instrument as the water is siphoned away from the bath and then replaced with colder
water in order to speed up the cooling of the bath water. As this required a brief reset of the
experimental setup and the instruments continuing to take readings as time went on, this
change at the T = 32 ℃ mark would be preferable to avoid by finding another system to
cool the existing bath temperature without having to displace water which works quite well
but has room for error and spillage.
Reference
[1] Yunus A. Cengel and Afshin J. Ghajar, Heat and Mass Transfer Fundamentls and
Applications 4th Ed., McGraw-Hill 2011, p.112-118
[2]"National Weather Service Weather Forecast Office." NWS Denver-Boulder, CO. N.p.,
n.d. Web. 20 Apr. 2014.
Appendix
Measurement
,i
Resistance, R
(kOhms)
Voltage, V
(mV)
Temperature
, T (°C)
Pressure, Psat (T)
(kpa)
Pressure, Psat =
a + bV
1
2
121.82
121.82
15.583
15.593
55.110
55.110
15.81
15.81
15.418
15.428
3
121.82
15.602
55.110
15.81
15.437
4
5
121.82
121.82
15.607
15.605
55.110
55.110
15.81
15.81
15.442
15.440
6
121.82
15.606
55.110
15.81
15.441
7
121.82
15.609
55.110
15.81
15.444
8
121.82
15.611
55.110
15.81
15.446
9
121.82
15.614
55.110
15.81
15.450
10
121.82
15.613
55.110
15.81
average
15.449
15.440
Measurement
,i
Resistance, R
(kOhms)
Voltage, V
(mV)
Temperature
, T (°C)
Pressure, Psat
(kpa)
Pressure, Psat =
a + bV
1
2
3
117.89
117.93
117.93
9.563
9.616
9.615
45.104
45.206
45.206
9.62
9.67
9.67
9.264
9.318
9.317
4
117.93
9.610
45.206
9.67
9.312
5
117.91
9.594
45.155
9.65
9.296
6
117.90
9.583
45.130
9.63
9.285
7
8
117.90
117.89
9.579
9.574
45.130
45.104
9.63
9.62
9.281
9.275
9
117.89
9.571
45.104
9.62
9.272
10
117.89
9.570
45.104
9.62
Measurement
,i
Resistance, R
(kOhms)
Voltage, V
(mV)
Temperature
, T (°C)
Pressure, Psat (T)
(kpa)
9.271
9.289
Pressure, Psat =
a + bV
1
112.79
5.016
32.166
4.79
4.616
2
112.79
4.999
32.166
4.79
4.599
3
112.79
4.985
32.166
4.79
4.585
4
112.79
4.977
32.166
4.79
4.576
5
6
112.79
112.79
4.968
4.959
32.166
32.166
4.79
4.79
4.567
4.558
7
8
112.79
112.79
4.951
4.944
32.166
32.166
4.79
4.79
4.550
4.543
9
112.79
4.936
32.166
4.79
4.534
10
112.79
4.624
32.166
4.79
4.216
4.534
Measurement
Resistance, R
Voltage, V
Temperature
Pressure, Psat (T)
Pressure, Psat =
,i
(kOhms)
(mV)
, T (°C)
(kpa)
a + bV
1
111.19
3.913
28.117
3.80
3.489
2
3
111.21
111.21
3.912
3.908
28.167
28.167
3.81
3.81
3.488
3.484
4
111.21
3.905
28.167
3.81
3.481
5
6
111.21
111.22
3.903
3.900
28.167
28.193
3.81
3.81
3.479
3.475
7
111.22
3.898
28.193
3.81
3.473
8
9
111.22
111.22
3.897
3.895
28.193
28.193
3.81
3.81
3.472
3.470
10
111.22
3.894
28.193
3.81
3.469
Measurement
,i
Resistance, R
(kOhms)
Voltage, V
(mV)
Temperature
, T (°C)
Pressure, Psat (T)
(kpa)
Pressure, Psat =
a + bV
1
110.06
3.295
25.260
3.21
2.857
2
3
4
110.07
110.07
110.07
3.297
3.299
3.301
25.286
25.286
25.286
3.21
3.21
3.21
2.859
2.861
2.863
5
6
7
111.21
110.07
110.08
3.302
3.303
3.304
28.167
25.286
25.311
3.81
3.21
3.22
2.864
2.865
2.866
8
9
10
110.08
110.08
110.08
3.305
3.306
3.307
25.311
25.311
25.311
3.22
3.22
3.22
2.867
2.868
2.869
2.864
Table 8: This table shows the calculations of mean experimental temperatures and their
corresponding experimental pressures.