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.

All the variables are functions of a clusius point at at time. 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. This page was last edited on 9 Augustat Rheology Viscoelasticity Rheometry Rheometer. Since is arbitrary, we must have. By using this site, you agree to the Terms of Use and Privacy Policy.

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

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.

This inequality is a statement concerning the irreversibility of natural processes, especially when energy dissipation is involved. 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, Now, the material time derivatives of and are given by Therefore, From the conservation of mass.

Surface tension Capillary action. 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. The Clausius—Duhem inequality can be expressed in integral form as.

Clausius–Duhem inequality – Wikipedia

This inequality is particularly useful in determining whether the constitutive relation of a material is thermodynamically allowable. The inequality can be expressed in terms of the internal energy as.

Surface tension Capillary action. Views Read Edit View history. This inequality is particularly useful in determining whether the constitutive relation of a material is thermodynamically allowable.

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.

Now, using index notation with respect to clauius Cartesian coordinate system. Hence the Clausius—Duhem inequality is also called the dissipation inequality. From the conservation of mass. Clausius—Duhem inequality Continuum mechanics. Rheology Viscoelasticity Rheometry Rheometer. In differential form the Clausius—Duhem inequality can be written as. Using the identity in the Clausius—Duhem inequality, we get Now, using index notation with respect to a Cartesian coordinate systemHence, From the infquality of energy Therefore, Rearranging.

From the balance of energy.

Using the divergence theoremwe get. In a real material, the dissipation is always greater than zero. The Clausius—Duhem inequality [1] [2] is a way of expressing the second law of thermodynamics that is used in continuum mechanics.

From the balance of energy. This inequality is a statement concerning the irreversibility of natural processes, especially when energy dissipation is duhfm. In differential form the Clausius—Duhem inequality can be written as. The inequality can be expressed in terms of the internal energy as.

Clausius–Duhem inequality

Now, the material time derivatives of and are given by. Assume that is an arbitrary fixed control volume. Retrieved from ” https: Using the divergence theoremwe get.