To some extent modern continuum thermodynamics amounts to a collection of “ thermodynamical theories” sharing common premisses and common. sources on Ωt. Total entropy: units [J/K], defined up to a constant by. dS = dQ. T. Clausius-Duhem inequality: mathematical form of the 2nd law: DS. Dt. ≥. ∫. Ωt. sθ is the specific dissipation (or internal dissipation) and is denoted by the symbol ϕ. The Clausius-Duhem inequality can simply be written as.

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Using the identity in the Clausius—Duhem inequality, we get Now, using index notation with respect to a Cartesian coordinate systemHence, From the balance of energy Therefore, Rearranging.

Surface tension Capillary action. Indquality page was last edited on 9 Augustat Rheology Viscoelasticity Rheometry Rheometer. Xuhem inequality can be expressed in terms of the internal energy as. From the conservation of mass. This inequality is particularly useful in determining whether the constitutive relation of a material is thermodynamically allowable.

Hence the Clausius—Duhem inequality is also called the dissipation inequality.

In differential form the Clausius—Duhem inequality can be written as. Using the divergence theoremwe get. Then and the derivative can be taken inside the integral to give Using the divergence theoremwe get Since is arbitrary, we must have Expanding out or, or, Inequailty, the material time derivatives of and are given by Therefore, From the conservation of mass.

From the balance of energy. This inequality is a statement concerning the irreversibility of natural processes, especially when energy dissipation is involved. Using the divergence theoremwe get. All the variables are functions of a material point at at time.

This inequality is particularly useful in determining whether the constitutive relation of a material is thermodynamically allowable.

The Clausius—Duhem inequality can be expressed in integral form as. In a real material, the dissipation is always greater than zero.

Hence the Clausius—Duhem inequality is also called the dissipation inequality. The Clausius—Duhem inequality [1] [2] is a way of expressing the second law of thermodynamics that is used in continuum mechanics. Views Read Edit View history. Clausius—Duhem inequality Continuum mechanics. From the balance of energy. Now, using index notation with respect to a Cartesian coordinate system. The inequality can be expressed in terms of the internal energy as.

This inequality incorporates the balance of energy and the balance of linear and angular momentum into the expression for the Clausius—Duhem inequality. Laws Conservations Energy Mass Momentum.

## Clausius–Duhem inequality

In differential form the Clausius—Duhem inequality infquality be written as. Rheology Viscoelasticity Rheometry Rheometer. Since is arbitrary, we must have. The Clausius—Duhem inequality can be expressed in integral form as. In a real material, the dissipation is always greater than zero. From Wikipedia, the free encyclopedia.

Laws Conservations Energy Mass Momentum. In this equation is the time, represents a body and the integration is over the volume of the body, represents the surface of the body, is the mass density of the body, is the specific entropy entropy per unit massis the normal velocity ofis the velocity of particles insideis the unit normal to the surface, is the heat flux vector, is an energy source per unit mass, and is the absolute temperature.

### Clausius–Duhem inequality

This inequality incorporates the balance of energy and the balance of linear and angular momentum into the expression for the Clausius—Duhem inequality. The Clausius—Duhem inequality [1] [2] is a way of dihem the second law of thermodynamics that is used in continuum mechanics. Now, the material time derivatives of and are given by.

Assume that is an arbitrary fixed control volume. Surface tension Capillary action. Retrieved from ” https: By using this site, you agree to the Terms of Use and Privacy Policy. This inequality is a statement concerning the irreversibility of natural processes, especially when energy dissipation is involved.