Rose–Vinet Equation Of State

	Rose–Vinet Equation Of State The Rose–Vinet equation of state is a set of equations used to describe the equation of state of solid objects. It is a modification of the Birch–Murnaghan equation of state. The initial paper discusses how the equation only depends on four inputs: the isothermal bulk modulus The bulk modulus (K or B) of a substance is a measure of how resistant to compression the substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting ''relative'' decrease of the volume. Other moduli describe ... B_0, the derivative of bulk modulus with respect to pressure B_0', the volume V_0, and the thermal expansion; all evaluated at zero pressure (P=0) and at a single (reference) temperature. The same equation holds for all classes of solids and a wide range of temperatures. Let the cube root of the specific volume be :\eta=\left(\right)^ then the equation of state is: :P=3B_0\left(\frac\right)e^ A similar equation was published by Stacey et al. in 1981. Re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Equation Of State In physics, chemistry, and thermodynamics, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equations of state are useful in describing the properties of pure substances and mixtures in liquids, gases, and solid states as well as the state of matter in the interior of stars. Overview At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the ideal gas law, which is roughly accurate for weakly polar gases at low pressures and moderate temperatures. This equation becomes increasingly inaccurate at higher pressures and lower temperatures, and fails to predict ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Birch–Murnaghan Equation Of State The Birch–Murnaghan isothermal equation of state, published in 1947 by Albert Francis Birch of Harvard, is a relationship between the volume of a body and the pressure to which it is subjected. Birch proposed this equation based on the work of Francis Dominic Murnaghan of Johns Hopkins University published in 1944, so that the equation is named in honor of both scientists. Expressions for the equation of state The third-order Birch–Murnaghan isothermal equation of state is given by P(V)=\frac \left left(\frac\right)^ - \left(\frac\right)^\right\left\. where ''P'' is the pressure, ''V''0 is the reference volume, ''V'' is the deformed volume, ''B''0 is the bulk modulus, and ''B''0' is the derivative of the bulk modulus with respect to pressure. The bulk modulus and its derivative are usually obtained from fits to experimental data and are defined as B_0 = -V \left(\frac\right)_ and B_0' = \left(\frac\right)_ The expression for the equation of state is obtained by expandi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Bulk Modulus The bulk modulus (K or B) of a substance is a measure of how resistant to compression the substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting ''relative'' decrease of the volume. Other moduli describe the material's response (strain) to other kinds of stress: the shear modulus describes the response to shear stress, and Young's modulus describes the response to normal (lengthwise stretching) stress. For a fluid, only the bulk modulus is meaningful. For a complex anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law. The reciprocal of the bulk modulus at fixed temperature is called the isothermal compressibility. Definition The bulk modulus K (which is usually positive) can be formally defined by the equation :K=-V\frac , where P is pressure, V is the initial volume of the substance, and dP/dV denotes the derivative of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Solid Mechanics Solid mechanics, also known as mechanics of solids, is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents. Solid mechanics is fundamental for civil, aerospace, nuclear, biomedical and mechanical engineering, for geology, and for many branches of physics such as materials science. It has specific applications in many other areas, such as understanding the anatomy of living beings, and the design of dental prostheses and surgical implants. One of the most common practical applications of solid mechanics is the Euler–Bernoulli beam equation. Solid mechanics extensively uses tensors to describe stresses, strains, and the relationship between them. Solid mechanics is a vast subject because of the wide range of solid materials available, such as steel, wood, concrete, biological materials, textiles, geological ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]