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Pressure of Fluids01:14

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There are many examples of pressure in fluids in everyday life, such as in relation to blood (high or low blood pressure) and in relation to weather (high- and low-pressure weather systems). A given force can have a significantly different effect, depending on the area over which the force is exerted. For instance, a force applied to an area of 1 mm2 has a pressure that is 100 times greater than the same force applied to an area of 1 cm2. That's why a sharp needle is able to poke through skin...
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The pV diagram, which is a graph of pressure versus volume of the gas under study, is helpful in describing certain aspects of the substance. When the substance behaves like an ideal gas, the ideal gas equation describes the relationship between its pressure and volume. On a pV diagram, it is common to plot an isotherm, which is a curve showing p as a function of V with the number of molecules and the temperature fixed. Then, for an ideal gas, the product of the pressure of the gas and its...
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The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
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Hydrophobic effect in the pressure-temperature plane.

Kenichiro Koga1

  • 1Department of Chemistry, Faculty of Science, Okayama University, Tsushima-Naka 3-1-1, Okayama 700-8530, Japan.

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|October 12, 2004
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Summary

This study explores hydrophobic hydration and solvent-mediated attraction using a lattice model. A key finding reveals a consistent relationship between hydration free energy and attraction strength across specific pressure-temperature conditions.

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Area of Science:

  • Thermodynamics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • The hydrophobic effect is crucial in biological and chemical systems.
  • Understanding solvent-mediated interactions is key to molecular behavior.
  • Existing models often simplify the complex interplay of temperature and pressure.

Purpose of the Study:

  • To calculate hydrophobic hydration free energy and solvent-mediated attraction strength.
  • To investigate these properties within a pressure-temperature (P-T) phase diagram.
  • To extend the Kolomeisky-Widom lattice model to include pressure as a thermodynamic variable.

Main Methods:

  • Utilizing an exactly soluble lattice model, an extension of the Kolomeisky-Widom model.
  • Incorporating mechanisms for both low-temperature hydrophobic effects and high-temperature solvation.
  • Analyzing the P-T plane to identify critical boundaries for solubility and attraction strength.

Main Results:

  • Two distinct, nearly linear, and parallel boundaries were identified in the P-T plane.
  • The first boundary defines conditions where solubility decreases with increasing temperature.
  • The second boundary indicates where solvent-mediated attraction strength increases with temperature.

Conclusions:

  • A universal, near-linear relationship exists between hydration free energy and hydrophobic attraction strength within a specific P-T region.
  • The extended lattice model provides a framework for understanding hydrophobic phenomena under varying pressure and temperature.
  • The identified boundaries offer insights into the phase behavior of hydrophobic interactions.