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Work and Energy for Variable Forces01:10

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When an object is acted upon by a variable force, the amount of work done and the change in energy of the object can be more complex to calculate compared to when a constant force is applied. Work is the product of force and displacement, while energy is the capacity of a system to do work. When a constant force is applied to an object, the work done can be calculated as the product of the force and the distance moved in the direction of the force. However, when a variable force is applied, the...
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Consider a particle moving under the action of a conservative force that has components along each coordinate axis. Each component of force is a function of the coordinates. The potential energy function U is also a function of all three spatial coordinates. Force in one dimension can be written as the negative ratio of potential energy change to the displacement along that coordinate. For minimal displacement, the ratios become derivatives. If a function has many variables, the derivative only...
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Applying the conservation of energy principle or the work-energy theorem to an incompressible, inviscid fluid in laminar, steady, irrotational flow leads to Bernoulli's equation. It states that the sum of the fluid pressure, potential, and kinetic energy per unit volume is constant along a streamline.
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Potential-Energy Criterion for Equilibrium01:16

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Potential energy or potential function plays an essential role in determining the stability of a mechanical system. If a system is subjected to both gravitational and elastic forces, the potential function of the system can be expressed as the algebraic sum of gravitational and elastic potential energy. If the system is in equilibrium and is displaced by a small amount, then the work done on the system equals the negative of the change in the system's potential energy from the initial to...
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Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...
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The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
 
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Some Recent Advances in Energetic Variational Approaches.

Yiwei Wang1, Chun Liu1

  • 1Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA.

Entropy (Basel, Switzerland)
|May 28, 2022
PubMed
Summary

This paper reviews the energetic variational approach (EnVarA) for creating thermodynamically consistent models for complex fluids. It highlights applications in chemo-mechanical couplings and non-isothermal systems.

Keywords:
chemo-mechanical couplingenergetic variational approachnon-equilibrium thermodynamicsthermal effects

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Area of Science:

  • Multiphysics modeling
  • Thermodynamics
  • Computational fluid dynamics

Background:

  • Complex fluids present modeling challenges due to their intricate behavior.
  • Existing models may lack thermodynamic consistency.
  • The energetic variational approach offers a unified framework.

Purpose of the Study:

  • To summarize recent advancements in the energetic variational approach (EnVarA).
  • To demonstrate EnVarA's utility in modeling complex fluid systems.
  • To focus on chemo-mechanical couplings and non-isothermal effects.

Main Methods:

  • Review of recent research and applications of EnVarA.
  • Illustrative examples of EnVarA in action.
  • Focus on variational principles and thermodynamic consistency.

Main Results:

  • EnVarA provides a robust framework for thermodynamically consistent models.
  • Successful application of EnVarA to systems with chemo-mechanical couplings.
  • Effective modeling of non-isothermal effects in complex fluids.

Conclusions:

  • EnVarA is a powerful and versatile tool for complex fluid modeling.
  • The approach ensures physical realism and thermodynamic rigor.
  • Further research can expand EnVarA's applicability to more complex phenomena.