Adiabatic Compressibility of Different Water Samples With Temperature Variations (281 K to 303k) – a Pilot Study

doi:10.21203/rs.3.rs-4829244/v1

Download PDF

Research Article

Adiabatic Compressibility of Different Water Samples With Temperature Variations (281 K to 303k) – a Pilot Study

https://doi.org/10.21203/rs.3.rs-4829244/v1

This work is licensed under a CC BY 4.0 License

You are reading this latest preprint version

The present work highlights the study of effect of temperature variation between (281–303 K) on ultrasonic velocity and adiabatic compressibility for three different water samples, tap water (TDS = 1060), RO water (TDS = 74) and distilled water (TDS = 06). Other factors analysed along with temperature variation and TDS (Total Dissolved Salts) were density and refractive index. All three water samples showed variations from usual trend in specific temperature ranges. Ultrasonic velocity showed a minor increase in tap water between (285–288K), instead of decreasing, similarly for RO water ultrasonic velocity varied as per comparison with literature review in the range (291–294K), and for distilled water ultrasonic velocity showed small variations between (286–287K). Density of the three water samples under study, showed a uniform decline with increase in temperature, highest value was observed for tap water 1000.716 kg/m³ and lowest for distilled water 995.706kg/m³. Regression Statistics yielded positive results for correlation between TDS and adiabatic compressibility for Tap water. Further studies on compressibility of water with varying salts, could pave way for new applications in hydraulics and shock absorption equipment’s.

Adiabatic Compressibility

Reverse Osmosis

TDS

Ultrasonic Velocity.

Liquids cannot be compressed much, reason being there is not much space between the molecules. Literature review [1–7] states that water is approximately incompressible, and the compressibility factor of water can be avoided when doing calculations. Low compressibility of water happens because of high density of water. [8– 9]. The compressibility factor finds numerous applications in our daily life specially hydraulics. Compressibility is basically, a measure of the relative volume change of a fluid in response to pressure change.

Aim of our study was to analyse the relation of compressibility factor for three samples of water which have different total dissolved solids (TDS) along with variation in temperature. The present study was carried out with water samples used in daily life, which vary according to TDS, three samples were taken Tap Water (TDS = 1060), Reverse Osmosis Water (RO) (TDS = 74) and Distilled Water (TDS = 06). With the help of ultrasonic interferometer ultrasonic velocity was studied with temperature variations in the range (281–303 K), along with density and refractive index. Once ultrasonic velocity was observed with temperature variations using an ultrasonic interferometer, adiabatic compressibility, acoustic impedance parameters were calculated and presented in the form of Table’s (1, 2, 3), for the three water samples.

Specific gravity bottle was used to measure density. Refractive index was measured with the help of Abbe’s refractometer. Regression Statistics was applied to find if any correlation existed between adiabatic compressibility and TDS along with temperature variations.

Measurement of physiochemical properties like ultrasonic velocity, adiabatic compressibility

acoustic impedance, density, TDS (Total Dissolved Salts), of different forms of water used by humans for various purposes are of great importance. As water is basic source of survival for life on earth. [10, 11].

TDS typically found in water are the mineral content, [12–13]. Water being a good solvent is prone to impurities easily. TDS (Total Dissolved Salts) present in our water sample comprise of minerals, inorganic salts, calcium, chemicals etc. Also, certain salts present dissolved in water at higher temperatures, showing minor changes in TDS (Tables 1, 2 and 3).

With increasing forms of water consumption available and different types of water plants being set up all over the country either for human consumption, or hydraulic purposes, quality of water and which is best suitable for survival of life will always remain a topic of research.

These days every home, office, public place etc are installed with RO filters of different types. [14–15] Distilled water is used for many medical and experimental purposes [16–17]. Also, tap water being supplied by water authorities is also used by humans for various purposes. The purpose of the present work is to analyse the physiochemical properties of three water samples differentiated on the basis of TDS present in them in the temperature range of (280–303K). Pure water samples with varying TDS, were purposely chosen for the study as they will help in providing appearance of new forms of water samples which can be beneficial for humans.

Regression analysis was done to find a correlation between TDS and adiabatic compressibility with temperature variations. The regression model helped us confirm the authenticity of our results, and showed a positive correlation when water sample with highest TDS (Tap water) was taken it showed a good correlation with adiabatic compressibility, paving way for more studies on adiabatic compressibility variations with TDS, study will be highly useful in designing hydraulic engines.

2.1 Experimental Technique

The experimental apparatus consisted of a single crystal interferometer, from Mittal Enterprises, New Delhi, operating at a frequency of 2MHz, with an accuracy of ± 1.0 m/s, the inlet outlet pipes fitted with the system help in taking readings with temperature variation. Total Dissolved Salts (TDS) were measured with the help of digital TDS meter, simple mercury thermometers were used to measure temperature variations they were inserted in the water bath. Densities of the solutions were measured using a 25 mL specific gravity bottle and the weight of the liquid was measured using an electronic balance (Model Shimadzu AX200). Abbes Refractometer was used to measure refractive index.

2.2 Theory

The acoustic parameters were calculated as follows.

The ultrasonic velocity is calculated as

v = fλ

where f is the frequency of the ultrasonic waves (2 MHz) and λ is the measured wavelength value of ultrasonic wave.

Adiabatic Compressibility

Adiabatic compressibility (𝛽) is calculated, from the ultrasonic velocity “v” and the density “𝜌” of the solution using the Newton-Laplace equation

$$\:\varvec{\beta\:}=\:\frac{1}{\varvec{\rho\:}{\varvec{v}}^{2}}$$

Acoustic impedance (𝑍) is analysed with the help of the following formula

𝑍=𝜌v,

where 𝜌 and v are the density and velocity of the solution, respectively.

The experimentally obtained values of density, TDS, refractive index, and ultrasonic velocity with varying temperature are reported in Tables 1, 2 and 3 for Tap Water, RO water and Distilled water respectively.

Table 1

Observations for Tap Water
Temperature	TDS	Refractive Index	UV Ultrasonic Velocity (v) (m/s)	Density (ρ) (kg/m³)	Adiabatic Compressibility (β) (m²/N)	Acoustic Impedance (Ry)
281K	1060	1.414	1480	1000.716	4.562E-10	1481059.68
282K	1060	1.414	1400	1000.645	5.099E-10	1400903
283K	1060	1.414	1480	1000.561	4.563E-10	1480830.28
284K	1060	1.414	1440	1000.464	4.82E-10	1440668.16
285K	1060	1.414	1480	1000.354	4.564E-10	1480523.92
286K	1060	1.414	1520	1000.231	4.327E-10	1520351.12

Table 2

Observations for RO Water
Temperature	TDS	Refractive Index	UV Ultrasonic Velocity (v) (m/s)	Density (ρ) (kg/m³)	Adiabatic Compressibility (β) (m²/N)	Acoustic Impedance (Ry)
277K	74	1.349	1520	1000.06	4.33E-10	1520091
281K	74	1.349	1480	999.935	4.57E-10	1479904
282K	74	1.349	1546	999.888	4.18E-10	1545827
283K	100	1.414	1466.66	999.807	4.65E-10	1466377
287K	100	1.414	1480	999.351	4.57E-10	1479039
288K	100	1.414	1440	999.206	4.83E-10	1438857
291K	83	1.414	1440	99.689	4.84E-09	143552.2
293K	113	1.36	1490	998.32	4.51E-10	1487497
294K	116	1.355	1600	998.111	3.91E-10	1596978
295K	116	1.355	1500	997.889	4.45E-10	1496834
296K	116	1.355	1584	997.657	3.99E-10	1580289
297K	116	1.356	1480	997.415	4.58E-10	1476174
298K	116	1.356	1496	997.163	4.48E-10	1491756
299K	116	1.356	1480	996.902	4.58E-10	1475415
300K	116	1.355	1573.33	996.631	4.05E-10	1568029
303K	116	1.358	1460	995.765	4.71E-10	1453817

Table 3

Observations for Distilled Water
Temperature	TDS	Refractive Index	UV Ultrasonic Velocity (v) (m/s)	Density (ρ) (kg/m³)	Adiabatic Compressibility (β) (m²/N)	Acoustic Impedance (Ry)
283K	06	1.36	1500	999.757	4.4455E-10	1499635.5
284K	06	1.36	1416	999.662	4.9891E-10	1415521.39
285K	06	1.36	1480	999.554	4.5674E-10	1479339.92
286K	06	1.36	1500	999.434	4.447E-10	1499151
287K	06	1.36	1840	999.301	2.9558E-10	1838713.84
293K	06	1.36	1488	998.261	4.5243E-10	1485412.37
296K	06	1.36	1480	997.596	4.5764E-10	1476442.08
298K	06	1.413	1500	997.102	4.4574E-10	1495653
299K	06	1.413	1666.66	996.841	3.6114E-10	1661395.02
303K	06	1.423	1613.33	995.706	3.8585E-10	1606402.36

Density depends on mass and volume, [18–19] temperature variations lead to changes in molecular associations, resulting in changes in mass and volume and hence density as shown in the Tables 1, 2 and 3. Under a set of experimental conditions the values of the three water samples, are affected by Total Dissolve Salts, Temperature .The regression and ANOVA statistics for Tap Water (highest TDS) and Adiabatic Compressibility are reported in Tables 4 and 5.Good correlation was observed in TDS and adiabatic compressibility of Tap Water.

Variation of adiabatic compressibility with temperature plotted for the three water samples, Tap Water, RO water and Distilled water have been shown in Figs. 1, 2 and 3 along with the trendline (dotted).

Figure 1, shows plot between adiabatic compressibility along with variation in temperature for tap water (TDS = 1060). The trendline line shows a uniform decline with temperature.

Figure 2 shows variation of adiabatic compressibility with variation in temperature for RO water carrying a TDS of 74. In temperature range (291 K – 294K) the graph shows a dip, while in the rest of the temperature range, the compressibility is constant. Trendline also shows a constancy throughout.

Figure 3 shows variation of adiabatic compressibility with variation in temperature for distilled water carrying a TDS of 06. A sharp dip was observed in the graph at 287K, while the trendline followed a pattern of minor decline.

3.1 Multiple Regression Analysis in Excel

While doing analysis with regression analysis [20] TDS was taken as independent variable and adiabatic compressibility as the dependent variable, regression analysis was performed for all the three samples, out of which positive correlation was found for tap water only while the other samples RO and distilled showed negative correlation.

Regression Statistics

Regression Statistics was applied to find the relation between adiabatic compressibility and TDS (Total Dissolved Salts) of the three water samples. The regression statistics for all three water samples (Tap water, RO water and Distilled Water) where temperature was taken as independent variable and adiabatic compressibility was taken as dependent variable showed very poor correlation. The correlation coefficient R, which measures the strength between the two variables (temperature and adiabatic compressibility) was found to be very poor 23% for Tap Water, approximately 0% for RO water, and 8% for distilled water.

Also, the F value (significance F), which states that if F value is less than 0.05 (5%) then model is acceptable. For all the three water samples F value was greater than 0.05 (0.26 for tap Water, 0.77 for RO water, 0.44 for distilled water, hence rejecting the possibility of correlation between temperature and adiabatic compressibility.

Regression Statistics yielded positive result for correlation between TDS and adiabatic compressibility for tap water. The correlation coefficient R was found to be 0.61(61%) and the F value (significance F) was found to be 0.034 (less than 0.05), this model finally passes the statistical test and comes under category of being acceptable.

Table 4

Regression Statistics between Tap Water and Adiabatic Compressibility
Regression Statistics
Multiple R	0.790675128
R Square	0.625167158
Adjusted R Square	0.55020059
Standard Error	0.165222699
Observations	7

The R-squared value of 62, indicates that our model accounts for 62% of the dependent variable’s variance. Usually, higher R-squared values are better. F value which shows that whether the model is acceptable or not (value should be less than 0.05), also passes the test of acceptability.

The standard error which shows how certain one can be of result, smaller the number, more certain one can be of result is 0.16, showing that the result comes in the range of being acceptable (smaller the number the more certain one can be of result).

Table 5

ANOVA Statistics for Tap Water and Adiabatic Compressibility
	Df	SS	MS	F	Significance F	df
Regression	1	0.227650155	0.227650155	8.339279392	0.034275401	Regression
Residual	5	0.136492702	0.02729854			Residual
Total	6	0.364142857				Total

In the ANOVA Table 5, for Tap water the F- test for overall significance, significance F is 0.03 (< 0.05) which shows that the model is acceptable.

Our p-value for the overall F-test is 8.33783E-09. Value being small is written in scientific notation. The E-09, indicates that we need to move the decimal point 09 places to the left. Hence, can conclude that our regression model as a whole is statistically significant.

We included variables in our model: TDS and Adiabatic Compressibility. The coefficient is approximately 4.64. The positive sign indicates that as TDS increases, adiabatic compressibility also tends to increase. There is a positive association between these two variables. For every one-unit increase in TDS, compressibility increases by an average of 4.64.

The trends in the variation of parameters derived from ultrasonic velocity and density at various temperature ranges for the three water samples having different TDS, showed a positive correlation between TDS and adiabatic compressibility for tap water (TDS = 1060). Till date literature survey shows that liquids have very minute or nil compressibility, and compressibility of water is often neglected in mathematical calculations. But our studies have found a statistically significant and positive correlation between TDS and adiabatic compressibility. but the present work paves way for future studies on relation between TDS and compressibility for designing medical instruments, engines, refrigerators, air conditioners etc. which are based on the concept of compressibility. Work paves way for finding new ways to control the compressibility of water samples with varying TDS which will result in new applications in hydraulic based equipment’s paving way for growth of new technology.

Funding: Not applicable.

Conflict of Interest: On behalf of all authors, the corresponding author states that there is no conflict of interest.

Ethical approval: Not applicable.

Informed consent: Not applicable

Contributions: Divya Ghildyal wrote the main text , while Manisha Chaudry prepared the tables, statistical analysis and formatting part. All authors reviewed the manuscript.

Competing Interests : The authors declare no competing interests.

Data Availability Statement: The dataset on ultrasonic velocity, temperature, refractive index is available with the author. As these experiments have been performed in the lab.

Lind S J, Stansby PK, Rogers BD, Lloyd PM (2015) Numerical predictions of water–air wave slam using incompressible–compressible smoothed particle hydrodynamics. Applied Ocean Research. https://doi.org/10.1016/j.apor.2014.11.001
Panel L. Vittoz , G. Oger , M. de Leffe , D. Le Touzé (2019) Comparisons of weakly-compressible and truly incompressible approaches for viscous flow into a high-order Cartesian-grid finite volume framework. Journal of Computational Physics: X. https://doi.org/10.1016/j.jcpx.2019.100015
Abdullah C, Corapcioglu MY (2008) Water Resources Research. Effect of compressibility on the rise velocity of an air bubble in porous media. https://doi.org/10.1029/2006WR005415
Juncu D, Árnadóttir Th, Geirsson H, Gunnarsson G (2019) Geophysical Journal International. The effect of fluid compressibility and elastic rock properties on deformation of geothermal reservoirs. https://doi.org/10.1093/gji/ggz011
Bradshaw A, Karl Schleicher (1976) Deep Sea Research and Oceanographic Abstracts. Compressibility of distilled water and seawater. https://doi.org/10.1016/0011-7471(76)90002-4
Zhu X, Xu B and Han Z (2016) Mathematical Problems in Engineering. Measurement and Prediction Method of Compressibility Factor at High Temperature and High Pressure. https://doi.org/10.1155/2016/4681918
Rodriguez C & Millero FJ (2012) Aquatic Geochemistry. Estimating the Density and Compressibility of Seawater to High Temperatures Using the Pitzer Equations doi:10.1007/s10498-012-9183-2
Priyadarshini A, Biswas A, Chakraborty D, Mallik BS (2020) J. Phys. Chem. B. Structural and Thermophysical Anomalies of Liquid Water: A Tale of Molecules in the Instantaneous Low- and High-Density Regions. https://doi.org/10.1021/acs.jpcb.9b11596
Beibei Lai, Siyuan Liu, John Cahir (2023) Liquids with High Compressibility. Advanced Materials. https://doi.org/10.1002/adma.202306521
Husain MZ (2015) Global Journal of Advanced research. Water: The most precious resource of our life. 2: 1436-1445
Kılıç Z (2020) The importance of water and conscious use of water. International Journal of Hydrology. doi: 10.15406/ijh.2020.04.00250
IslamM, Sarkar M K, Afrin T (2016) A Study on the Total Dissolved Solids and Hardness Level of Drinking Mineral Water in Bangladesh. American Journal of Applied Chemistry DOI:10.11648/J.AJAC.20160405.11
Devesa R, Dietrich AM (2018) Guidance for optimizing drinking water taste by adjusting mineralization as measured by total dissolved solids (TDS). Desalination. https://doi.org/10.1016/j.desal.2018.04.017
Pangarkar BL, Mukund GS, and Guddad M (2011) A Reverse Osmosis and Membrane Distillation for Desalination of Groundwater: A Review. International Scholarly Research Network. doi:10.5402/2011/523124
Nikhil BA, Ramesh S, Dhanasekar S and Sudarsan JS (2017) Analysis and Treatment of Reverse Osmosis (RO) Reject From Dye Industries Using Anaerobic Baffled Reactor. RASAYAN Journal of Chemistry. doi:10.7324/RJC.2017.1041729
True RH (1914) American Journal of Botany. The Harmful Action of Distilled Water. https://doi.org/10.2307/2435102
Tillaart SAHMV, Busard MPH, Trimbos JBMZ (2009) Gynecol Surg. The use of distilled water in the achievement of localhemostasis during surgery. doi: 10.1007/s10397-008-0464-0
Oskui SM, Bhakta H, Diamante GY, Grover WH (2017) Measuring the mass, volume, and density of microgram-sized objects in fluid. PLOS ONE. https://doi.org/10.1371/journal.pone.0174068
Laraño JM, Ordóñez RM, Blanckenhorn WU, Montraveta CF (2008) Analysing body condition: mass, volume or density? Journal of Animal Ecology. https://doi.org/10.1111/j.1365-2656.2008.01433.x
Uyanık GK , Güler N (2013) A Study on Multiple Linear Regression Analysis. Procedia - Social and Behavioral Sciences. https://doi.org/10.1016/j.sbspro.2013.12.027

No competing interests reported.

Download PDF

Editorial decision: Revision requested
18 Aug, 2024
Reviews received at journal
18 Aug, 2024
Reviewers agreed at journal
17 Aug, 2024
Reviews received at journal
14 Aug, 2024
Reviewers agreed at journal
13 Aug, 2024
Reviewers invited by journal
13 Aug, 2024
Editor assigned by journal
12 Aug, 2024
Submission checks completed at journal
09 Aug, 2024
First submitted to journal
30 Jul, 2024

You are reading this latest preprint version

Adiabatic Compressibility of Different Water Samples With Temperature Variations (281 K to 303k) – a Pilot Study

Status:

Version 1

Abstract

Figures

1 INTRODUCTION

2 Materials and Methods

2.1 Experimental Technique

2.2 Theory

3 Results and Discussion

3.1 Multiple Regression Analysis in Excel

4 Conclusions

Declarations

References

Additional Declarations

Status:

Version 1