|
Thermal Pressure
In thermodynamics, thermal pressure (also known as the thermal pressure coefficient) is a measure of the relative pressure change of a fluid or a solid as a response to a temperature change at constant volume. The concept is related to the Pressure-Temperature Law, also known as Amontons's law or Gay-Lussac's law. In general pressure, (P) can be written as the following sum: P_\text(V,T) = P_\text(V,T) + \Delta P_\text(V,T). P_\text is the pressure required to compress the material from its volume V_0 to volume V at a constant temperature T_0. The second term expresses the change in thermal pressure \Delta P_ . This is the pressure change at constant volume due to the temperature difference between T_0 and T. Thus, it is the pressure change along an isochore of the material. The thermal pressure \gamma_v is customarily expressed in its simple form as \gamma_v =\left( \frac \right)_. Thermodynamic definition Because of the equivalences between many properties and derivatives w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology. Historically, thermodynamics developed out of a desire to increase the efficiency of early steam engines, particularly through the work of French physicist Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win the Napoleonic Wars. Scots-Irish physicist Lord Kelvin was the first to formulate a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal Pressure 1
A thermal column (or thermal) is a rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example of convection, specifically atmospheric convection. Thermals on Earth The Sun warms the ground, which in turn warms the air directly above. The warm air near the surface expands, becoming less dense than the surrounding air. The lighter air rises and cools due to its expansion in the lower pressure at higher altitudes. It stops rising when it has cooled to the same temperature, thus density, as the surrounding air. Associated with a thermal is a downward flow surrounding the thermal column. The downward-moving exterior is caused by colder air being displaced at the top of the thermal. The size and strength of thermals are influenced by the properties of the lower atmosphere (the ''troposphere''). When the air is cold, bubbles of warm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and even by industry. Further, both spellings are often used ''within'' a particular industry or country. Industries in British English-speaking countries typically use the "gauge" spelling. is the pressure relative to the ambient pressure. Various units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the SI unit of pressure, the pascal (Pa), for example, is one newton per square metre (N/m2); similarly, the pound-force per square inch (psi) is the traditional unit of pressure in the imperial and U.S. customary systems. Pressure may also be expressed in terms of standard atmospheric pressure; the atmosphere (atm) is equal to this pressure, and the torr is defined as of this. Manometric u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strain Tensor
In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness) at each point of space can be assumed to be unchanged by the deformation. With this assumption, the equations of continuum mechanics are considerably simplified. This approach may also be called small deformation theory, small displacement theory, or small displacement-gradient theory. It is contrasted with the finite strain theory where the opposite assumption is made. The infinitesimal strain theory is commonly adopted in civil and mechanical engineering for the stress analysis of structures built from relatively stiff elastic materials like concrete and steel, since a common goal in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasi-harmonic Approximation
The quasi-harmonic approximation is a phonon-based model of solid-state physics used to describe volume-dependent thermal effects, such as the thermal expansion. It is based on the assumption that the harmonic approximation holds for every value of the lattice constant, which is to be viewed as an adjustable parameter. Overview The quasi-harmonic approximation expands upon the harmonic phonon model of lattice dynamics. The harmonic phonon model states that all interatomic forces are purely harmonic, but such a model is inadequate to explain thermal expansion, as the equilibrium distance between atoms in such a model is independent of temperature. Thus in the quasi-harmonic model, from a phonon point of view, phonon frequencies become volume-dependent in the quasi-harmonic approximation, such that for each volume, the harmonic approximation holds. Thermodynamics For a lattice, the Helmholtz free energy ''F'' in the quasi-harmonic approximation is F(T,V) = E_(V) + U_(T,V) - T S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mie–Grüneisen Equation Of State
The Mie–Grüneisen equation of state is an equation of state that relates the pressure and volume of a solid at a given temperature.Roberts, J. K., & Miller, A. R. (1954). Heat and thermodynamics (Vol. 4). Interscience Publishers.Burshtein, A. I. (2008). Introduction to thermodynamics and kinetic theory of matter. Wiley-VCH. It is used to determine the pressure in a shock-compressed solid. The Mie–Grüneisen relation is a special form of the Grüneisen model which describes the effect that changing the volume of a crystal lattice has on its vibrational properties. Several variations of the Mie–Grüneisen equation of state are in use. The Grüneisen model can be expressed in the form :\Gamma = V \left(\frac\right)_V where is the volume, is the pressure, is the internal energy, and is the Grüneisen parameter which represents the thermal pressure from a set of vibrating atoms. If we assume that is independent of and , we can integrate Grüneisen's model to get : p - ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal Pressure 22
A thermal column (or thermal) is a rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example of convection, specifically atmospheric convection. Thermals on Earth The Sun warms the ground, which in turn warms the air directly above. The warm air near the surface expands, becoming less dense than the surrounding air. The lighter air rises and cools due to its expansion in the lower pressure at higher altitudes. It stops rising when it has cooled to the same temperature, thus density, as the surrounding air. Associated with a thermal is a downward flow surrounding the thermal column. The downward-moving exterior is caused by colder air being displaced at the top of the thermal. The size and strength of thermals are influenced by the properties of the lower atmosphere (the ''troposphere''). When the air is cold, bubbles of warm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Debye Model
In thermodynamics and solid-state physics, the Debye model is a method developed by Peter Debye in 1912 for estimating the phonon contribution to the specific heat (Heat capacity) in a solid. It treats the vibrations of the atomic lattice (heat) as phonons in a box, in contrast to the Einstein photoelectron model, which treats the solid as many individual, non-interacting quantum harmonic oscillators. The Debye model correctly predicts the low-temperature dependence of the heat capacity of solids, which is proportional to T^3 – the Debye ''T'' 3 law. Just like the Einstein photoelectron model, it also recovers the Dulong–Petit law at high temperatures. But due to simplifying assumptions, its accuracy suffers at intermediate temperatures. Derivation The Debye model is a solid-state equivalent of Planck's law of black body photon radiation, where one treats electromagnetic photonic radiation as a photon gas. The Debye model treats atomic vibrations as phonons in a box ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van Der Waals Equation
In chemistry and thermodynamics, the Van der Waals equation (or Van der Waals equation of state) is an equation of state which extends the ideal gas law to include the effects of interaction between molecules of a gas, as well as accounting for the finite size of the molecules. The ideal gas law treats gas molecules as point particles that interact with their containers but not each other, meaning they neither take up space nor change kinetic energy during collisions (i.e. all collisions are perfectly elastic). The ideal gas law states that the volume ''V'' occupied by ''n'' moles of any gas has a pressure ''P'' at temperature ''T'' given by the following relationship, where ''R'' is the gas constant: :PV=nRT To account for the volume occupied by real gas molecules, the Van der Waals equation replaces V/n in the ideal gas law with (V_m-b), where ''Vm'' is the molar volume of the gas and ''b'' is the volume occupied by the molecules of one mole: :P(V_m - b)=R T The second m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virial Theorem
In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by potential forces, with that of the total potential energy of the system. Mathematically, the theorem states \left\langle T \right\rangle = -\frac12\,\sum_^N \bigl\langle \mathbf_k \cdot \mathbf_k \bigr\rangle where is the total kinetic energy of the particles, represents the force on the th particle, which is located at position , and angle brackets represent the average over time of the enclosed quantity. The word virial for the right-hand side of the equation derives from ''vis'', the Latin word for "force" or "energy", and was given its technical definition by Rudolf Clausius in 1870. The significance of the virial theorem is that it allows the average total kinetic energy to be calculated even for very complicated systems that defy an exact solution, such as those considered in statistical mechanics; thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Transition
In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure. This can be a discontinuous change; for example, a liquid may become gas upon heating to its boiling point, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point. Types of phase transition At the phase transition point for a substance, for instance the boiling point, the two phases involved - liquid and vapor, have identic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isothermal Compressibility
In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change. In its simple form, the compressibility \kappa (denoted in some fields) may be expressed as :\beta =-\frac\frac, where is volume and is pressure. The choice to define compressibility as the negative of the fraction makes compressibility positive in the (usual) case that an increase in pressure induces a reduction in volume. The reciprocal of compressibility at fixed temperature is called the isothermal bulk modulus. Definition The specification above is incomplete, because for any object or system the magnitude of the compressibility depends strongly on whether the process is isentropic or isothermal. Accordingly, isothermal compressibility is defined: :\beta_T=-\frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
