Introduction
The object of the paper is to analyze the above relationship over a range of pressures extending above and below atmospheric pressure.
Data were obtained for the pressure and temperature of a saturated steam-water mixture in equilibrium over a wide range of pressures and temperatures. The “raw” experimental data are given at the end of this document and the apparatus used are described below.
The object of this exercise is to:
a) Use the raw data to produce a table of absolute pressure .v. absolute (thermodynamic) saturation temperature over the whole range of the data provided.
b) Compare this data to equivalent data taken from steam tables.
c) Use the data, along with the integrated form of the “Clausius-Clapeyron” equation to approximate the specific enthalpy of evaporation of water in the range of the experimental data. And compare this value with that obtained from steam tables.
d) Discuss the validity of all the assumptions used in c) above, as well as the uncertainties in the experimental data.
(a) Pressures above atmospheric
(b) Pressure below atmospheric
When evaluating these results, some experimental procedures will be applied to practice, in order to get to know if these procedures are possible to be developed.
Background Theory
Vapor–liquid equilibrium (VLE) is a definite condition when a liquid and the vapor (gas phase) stand in the equilibrium, according to the condition or state, where rates of evaporation (changing to vapor) are equal with the rates of condensations (vapor changing to liquids) on some molecular level. (Seader 1998)There is no net of the vapor–liquid interconversion. Some substances at the vapor–liquid equilibriums are generally referred to the saturated fluid. As for pure chemical substances, this statement, according to some researchers (Balzhiser 1972; Smith 2005) is implied to the boiling point. The concept of the "saturated fluid" includes the saturated liquids (that are about to vaporize), the saturated liquid and vapor mixtures, and the saturated vapors are about to being condensed (DePriester 2003).
Although the theory of equilibrium is still not so much researched, so an equilibrium may be practically reached, as for the relatively closed locations, in case if liquids and their vapors are allowed standing in contacts with each other, with no interference, at only the gradual interference.
Materials and Apparatus
The materials that will be used to provide the experiments are the following:
- Steel
- Water
- Glass
The equipments that will be used to provide the experiments are the following:
- A small steel pressure vessel;
- External heat source;
- Valve (on top of the boiler);
- Small quantity of steam;
- Thermometer;
- Bourdon pressure gauge
The materials and equipments are useful to get good results via experiments. These materials and equipments are the best for lab experiments, as they are easy to handle.
Experimental Procedure
A small steel pressure vessel containing water was heated with an external heat source. With the valve (on top of the boiler) open, the water was raised to its boiling point and a small quantity of steam was blown off in order to expel air. When the thermometer attained a steady reading the temperature was recorded.
The valve was closed and heating continued until the gauge pressure read around 480 kPa. By regulating the heating rate, the pressure was held steady until the thermometer reading became steady. The temperature and pressure were then read using a mercury-in-glass thermometer and a bourdon pressure gauge.
The heat source was removed and the gauge pressure allowed falling to around 420 kPa. The heat source was then applied intermittently until the temperature was steady, and temperature and pressure again recorded.
The process was repeated at intervals of about 60 kPa down to a gauge pressure of around 60 kPa.
Results
(b) Pressures below atmospheric
A sealed glass vacuum chamber contained a beaker of water into which was placed an electric immersion heater supplied via a variac (variable voltage supply). A water vacuum pump is used to lower the pressure in the glass vessel while the pressure is measured using a mercury-in-glass manometer. Temperature is measured using a mercury-in-glass thermometer.
With the vacuum chanber open to atmosphere, the variac was set to maximum and the water brought to the boil. When a steady temperature was reached the thermometer and manometer were read.
The vacuum release valve was closed and the valve connecting the vacuum chanber to the water vacuum pump opened so that the pressure in the chamber was reduced to below atmospheric. When a vacuum of about 80 mmHg (difference between mercury levels) was reached, the valve connecting the pump and vacuum chamber was partially closed and adjusted continually so as to hold the pressure constant while the thermometer attained a steady reading. The manometer and thermometer were again read. The procedure was repeated at a vacuum of about 160 mmHg. Further readings at intervals of about 80 mmHg up to the maximum vacuum which could be achieved were taken.
Analysis of Results
Plot temperature (as ordinate), against absolute pressure. The results of (a) and (b) should be shown on the same graph. Do not draw a line through the experimental points but show, as a line (i.e. without indicating the points used for plotting) values given in tables.
For equilibrium between two phases of a pure substance, the “Clausius-Clapeyron” equation, relates exactly, certain properties. For equilibrium between liquid and vapour:
(dP /dT)sat = hfg / (Tvfg)
where:-
hfg = specific enthalpy of evaporation (“latent heat”)
T = temperature
P = pressure (i.e. “absolute pressure”)
Vg = specific volume of vapour phase
Vfg = vg – vf
Assuming that: (a) vg » vf , (b) the vapour phase is an ideal gas and (c) hfg is constant, the Clausius-Clapeyron equation may be integrated to give:
lnP-Hfg / (RT) + constant,
where R is the specific ideal-gas constant.
Plot ln (P/Pa), as ordinate, against T-1 / K-1 and hence, using the value of R for water given in tables, obtain a mean value of hfg for water over the experimental temperature range. Compare this with values given in tables.
Notes:
The report should include:-
(1) A description of the apparatus with diagrams,
(2) A description of the experimental procedure, and
(3) Derivations of equations (1) and (2).
Figures (including graphs) should be numbered consecutively Fig. 1, Fig. 2, etc. and should have titles.
The discussion of the results should include comments on the range of validity of assumptions (a), (b) and (c).
[Note: 1 mmHg may be taken as 133.3 Pa].
Raw experimental data
Barometer reading = 760.65 mmHg
(assume constant)
READINGS ABOVE ATMOSPHERIC PRESSURE
Gauge pressure / kPa T / oC
480 158
420 155
360 150
300 145
240 139
180 131
120 123
60 113
READINGS BELOW ATMOSPHERIC PRESSURE
Manometer reading / mmHg T / oC
80 98
160 95
240 91
320 87
400 82
480 76
560 69
640 58
740 25
Pressure units
1 mmHg = 9.8066513.5951 Pa (exactly, by definition) = 133.32 Pa (approx.)
1 inHg = 9.80665 13.5951 25.4 Pa (exactly, by definition)
= 3386.4 Pa (approx.). Use when converting barometer reading to Pa
1 bar = 100000 Pa
Pressure corresponding to a column of liquid of height h is h g
The density of mercury depends on temperature and the specific force of gravity g depend on location. However, for the purposes of this experiment, both are sufficiently close to the values used in the definition of “mmHG” that h/mmHg in the low-pressure experiment, may be taken as giving the pressure difference in mmHg.Discussion
According to the raw results of the provided experiments, it is worth to point out that comparative analysis of these data shows the possibility of the unique discussion on the matter. When evaluating the results of experiments, it is worth to remember, that the gotten data are presented in approximate environment only, so the further development of the ideas on the matter is possible by the further experiments in this field. It is worth to point out that more experiments should be provided on this matter.
However, we should present at least some bullet point related to this discussion, including:
READINGS ABOVE ATMOSPHERIC PRESSURE
- The ranges of minimum/maximum temperature/pressure of the experiments are between the wide ranges. For example, as it is seen from the raw results section, it turns clear that:
Minimum pressure rate – 60 kPa, while temperature - 113 oC;
Maximum pressure rate – 120 kPa, while the temperature - 123 oC;
Minimum temperature rate – 113 oC, while the pressure - 60 kPa;
Maximum temperature rate – 480 oC, while pressure - 158 kPa.
The water boils at 1000C. According to the steam table, the density of water at approx. of this rate is 618 gm/m3. If we analyze some other liquids, some of them have the higher density, so in this relation, it is clear that the temperatures of their boiling may vary, according to the steam table.
READINGS BELOW ATMOSPHERIC PRESSURE
- The ranges of minimum/maximum temperature/pressure of the experiments are between the wide ranges. For example, as it is seen from the raw results section, it turns clear that:
Manometer reading / mmHg
T / oC
Minimum pressure rate 80 mmHg, while temperature – 98 oC
Maximum pressure rate – 740 kPa, while the temperature - 25 oC;
Minimum temperature rate – 25 oC, while the pressure - 740 mmHg
Maximum temperature rate – 98 oC, while pressure - 80 kPa.
Saturated Vapor Pressure, Density for Water
Here some selected temperature is presented and the rates of the saturated vapor pressures that are required are presented in the places of the boiling points at these temperatures. The pressure rates are presented in the mega-Pascals, Pascal= a Newton per square meter, according to the standards of the atmospheric pressure.
TV Diagram for Heating H2O at Constant Pressure (Figure 2-11):
Pressure Cooker example: if the boiling temperature differs from the pressure rates.
Saturation Temperature: the boiling temperature in the given pressure.
Saturation Pressure: the pressure when boiling occurs at a given T.
Liquid-Vapor Saturation Curve for Water (Figure 2-12):
T-v Diagrams are useful to study and understand the phase of the changing processes. For the water liquid see the (Figure 2-13):
CRITICAL POINTS:
The saturated liquids and saturated states of vapor tend to be identical. No saturated mixture exists, since the substances change directly from liquids to the vapor states.
Let’s take a look at the Table A-1:
For H2O:
- PCR = 22.09 MPa
- TCR = 374.14 oC (or 647.3 oK)
- vCR = 0.003155 m3/kg (or .0568 m3/kmol)
The more T-v diagrams are presented in: (Figure 2-15):
P-v diagrams are shown: (Figure 2-16): Note: the rates of the constant temperature lines tend to downward.
P-T DIAGRAM (Figure 2-22): TRIPLE POINT
ENTHALPY, H
- the property of pure substances (internal energy, U);
- U is described as a function ONLY as the temperature of this substance;
- H is created in a way of combining U, the internal energy, and the work is done according to the form, PV. PV = (N/m2) (m3) = N-m = Joules;
- h = u + Pv (specific enthalpy)
- H is an appropriate function of both pressure and temperature.
Using the Clausius-Clapeyron equation, it is possible to get the results evaluated. Assuming that: (a) vg » vf , (b) the vapour phase is an ideal gas and (c) hfg is constant, the Clausius-Clapeyron equation may be integrated to give:
lnP-Hfg / (RT) + constant,
where R is the specific ideal-gas constant.
Plot ln (P/Pa), as ordinate, against T-1 / K-1 and hence, using the value of R for water given in tables, obtain a mean value of hfg for water over the experimental temperature range. Compare this with values given in tables.
PROPERTY TABLES
- They are used to look through the properties for the variety of substances at the various rates of temperature and pressure.
- In the tables, the saturated water rates are presented, according to the pressure rates and according to the steam tables that show the possibility of operating with the results very effectively.
vf = saturated LIQUID (volume).
vg = saturated VAPOR (volume).
vfg = the significant difference in the ranges of specific volumes of the saturated vaporings and saturated liquids = (vg - vf)
It is better to define the quality, and in the reference, the QUALITY, x, is never used to describe the compressed liquids or superheated vapors!!
Quality can be expressed in a percentage: in the range between 0%-100%, where 0% is a rate of the saturated liquid and 100% is a rate of the saturated vapor.
is treated as
The validity of the data and results
According to the results of the experiments, there is not much doubt that these data of the experiments are not valid. This can be proved via comparison of the results with the results of the experiments that are gotten via other experiments. The validity of the results of the experiments can be proved via comparing the results with the data in the steam tables. The data are valid, but there is also the degree of the uncertainty on this matter. There may be some degree of uncertainty in relevance to the calculations and chemical structures that can be added to get better results or some other that can even spoil experiments.
Conclusion
In the context of thermodynamics, and in relation to the results of this study, it was found out that experiments are valid and reliable. According to the results of the experiments, the conclusions should stand differently with the discussion. Water evaporation rates, temperature and pressure rates are the main data that were included to the improvised tables. The results were summarized according to the principles of the use of evaluation. The readings above and below atmospheric pressures are the main concepts that are useful to evaluate the results of this study.
Reference List
Balzhiser et al. 1972, Chemical Engineering Thermodynamics.
Seader, J. D., and Henley, EJ 1998, Separation Process Principles. New York: Wiley.
Smith JM, Van Ness, HC, & Abbott, MM 2005. Introduction to Chemical Engineering Thermodynamics (Seventh ed.). Boston: McGraw Hill.
DePriester CL 2003, Chem. Eng. Prog. Symposium Series, 7, 49, pages 1–43.
