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Constant Pressure Calorimetry03:02

Constant Pressure Calorimetry

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Calorimetry is a technique used to measure the amount of heat involved in a chemical or physical process or to measure the heat transferred to or from a substance. The heat is exchanged with a calibrated and insulated device called the calorimeter. Calorimetry experiments are based on the assumption that there is no heat exchange between the insulated calorimeter and the external environment. The well-insulated calorimeters prevent the transfer of heat between the calorimeter and its external...
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Fluid Pressure over Curved Plate of Constant Width01:12

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When a curved plate of constant width is submerged in a liquid, the pressure acting normal to the plate varies continuously both in magnitude and direction. Calculating the magnitude and location of the resultant force at a point is often challenging for such cases. One of the methods to determine the resultant force and its location involves separately calculating the horizontal and vertical components of the resultant force. This complex calculation can be simplified by representing the...
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Fluid Pressure over Flat Plate of Constant Width01:05

Fluid Pressure over Flat Plate of Constant Width

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When a body is submerged in water, it experiences fluid pressure acting normal on its surface and distributed over its area. For better design structures, it is crucial to determine the magnitude and location of the resultant force acting on the surface. In the case of a rectangular plate of constant width submerged in water, the pressure increases with depth, resulting in a linearly varying trapezoidal pressure distribution from the upper to the lower edge of the plate.
The resultant force...
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Calorimeters are useful to determine the heat released or absorbed by a chemical reaction. Coffee cup calorimeters are designed to operate at constant (atmospheric) pressure and are convenient to measure heat flow (or enthalpy change) accompanying processes that occur in solution at constant pressure. A different type of calorimeter that operates at constant volume, colloquially known as a bomb calorimeter, is used to measure the energy produced by reactions that yield large amounts of heat and...
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The concept of static, stagnation, dynamic, and total pressure is fundamental in fluid dynamics, often explained using Bernoulli's equation:
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Calculating the Equilibrium Constant02:46

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The equilibrium constant for a reaction is calculated from the equilibrium concentrations (or pressures) of its reactants and products. If these concentrations are known, the calculation simply involves their substitution into the Kc expression.
For example, gaseous nitrogen dioxide forms dinitrogen tetroxide according to this equation:
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Constant-pressure nested sampling with atomistic dynamics.

Robert J N Baldock1, Noam Bernstein2, K Michael Salerno3

  • 1Theory and Simulation of Materials (THEOS), and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.

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Summary

This study enhances the nested sampling algorithm for calculating material phase diagrams by introducing efficient all-particle Monte Carlo moves. This significantly reduces computational cost for determining phase transition temperatures in complex systems.

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Area of Science:

  • Computational Materials Science
  • Statistical Mechanics
  • Chemical Physics

Background:

  • The nested sampling algorithm is a powerful tool for calculating pressure-temperature-composition phase diagrams.
  • Previous implementations using single-particle Monte Carlo moves are computationally inefficient for condensed systems with general interactions.

Purpose of the Study:

  • To enhance the nested sampling algorithm for improved efficiency in calculating phase diagrams.
  • To introduce and evaluate all-particle Monte Carlo moves, specifically Galilean Monte Carlo and total enthalpy Hamiltonian Monte Carlo, for condensed systems.

Main Methods:

  • Implementation of all-particle moves (Galilean Monte Carlo, total enthalpy Hamiltonian Monte Carlo) within the nested sampling framework.
  • Comparison of computational cost and accuracy against single-particle Monte Carlo methods.
  • Application to various systems including Lennard-Jones, copper-gold alloy, water, and polymers.

Main Results:

  • All-particle moves reduce computational cost by a factor of N for N-particle systems with general interactions, achieving equivalent accuracy.
  • Demonstrated speed-up for freezing and condensation transitions in Lennard-Jones systems.
  • Successful calculation of diverse phase transitions, including order-disorder, eutectic, density anomaly, and polymer transitions.

Conclusions:

  • The enhanced nested sampling algorithm with all-particle moves offers a significant computational advantage for phase diagram calculations.
  • The new algorithms enable accurate determination of phase transition temperatures at reduced cost.
  • The pymatnest software package now incorporates these advanced algorithms for broader applicability.