In physics and chemistry, 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.
In thermodynamics, the specific heat capacity of a substance is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. It is also referred to as massic heat capacity or as the specific heat. More formally it is the heat capacity of a sample of the substance divided by the mass of the sample. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg−1⋅K−1. For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg−1⋅K−1.
Relative density, also called specific gravity, is a dimensionless quantity defined as the ratio of the density of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest ; for gases, the reference is air at room temperature. The term "relative density" is often preferred in scientific usage, whereas the term "specific gravity" is deprecated.
In fluid mechanics, hydrostatic equilibrium is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planetary physics of Earth, the pressure-gradient force prevents gravity from collapsing the planetary atmosphere into a thin, dense shell, whereas gravity prevents the pressure-gradient force from diffusing the atmosphere into outer space. In general, it is what causes objects in space to be spherical.
In fluid mechanics, the Grashof number is a dimensionless number which approximates the ratio of the buoyancy to viscous forces acting on a fluid. It frequently arises in the study of situations involving natural convection and is analogous to the Reynolds number.
The molar gas constant is denoted by the symbol R or R. It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per amount of substance, rather than energy per temperature increment per particle. The constant is also a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. It is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation.
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. The requirement of zero interaction can often be relaxed if, for example, the interaction is perfectly elastic or regarded as point-like collisions.
In chemistry and related fields, the molar volume, symbol Vm, or of a substance is the ratio of the volume occupied by a substance to the amount of substance, usually given at a given temperature and pressure. It is equal to the molar mass (M) divided by the mass density (ρ):
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At 20 °C (68 °F), the speed of sound in air is about 343 m/s, or one km in 2.91 s or one mile in 4.69 s. It depends strongly on temperature as well as the medium through which a sound wave is propagating. At 0 °C (32 °F), the speed of sound in air is about 331 m/s. More simply, the speed of sound is how fast vibrations travel.
Geopotential height or geopotential altitude is a vertical coordinate referenced to Earth's mean sea level that represents the work involved in lifting one unit of mass over one unit of length through a hypothetical space in which the acceleration of gravity is assumed constant. In SI units, a geopotential height difference of one meter implies the vertical transport of a parcel of one kilogram; adopting the standard gravity value, it corresponds to a constant work or potential energy difference of 9.80665 joules.
The van der Waals equation, named for its originator, the Dutch physicist Johannes Diderik van der Waals, is an equation of state that extends the ideal gas law to include the non-zero size of gas molecules and the interactions between them. As a result the equation is able to model the phase change from liquid to gas, and vice versa. It also produces simple analytic expressions for the properties of real substances that shed light on their behavior. One common way to write this dimensional equation is:
The density of air or atmospheric density, denoted ρ, is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variations in atmospheric pressure, temperature and humidity. At 101.325 kPa (abs) and 20 °C, air has a density of approximately 1.204 kg/m3 (0.0752 lb/cu ft), according to the International Standard Atmosphere (ISA). At 101.325 kPa (abs) and 15 °C (59 °F), air has a density of approximately 1.225 kg/m3 (0.0765 lb/cu ft), which is about 1⁄800 that of water, according to the International Standard Atmosphere (ISA). Pure liquid water is 1,000 kg/m3 (62 lb/cu ft).
The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change. For a given set of reaction conditions, the equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture. Thus, given the initial composition of a system, known equilibrium constant values can be used to determine the composition of the system at equilibrium. However, reaction parameters like temperature, solvent, and ionic strength may all influence the value of the equilibrium constant.
The virial expansion is a model of thermodynamic equations of state. This model expresses the pressure P of a gas in local equilibrium as a power series of the density. This equation may be represented in terms of the compressibility factor, , as
In atmospheric, earth, and planetary sciences, a scale height, usually denoted by the capital letter H, is a distance over which a physical quantity decreases by a factor of e.
In thermodynamics, the specific volume of a substance is a mass-specific intrinsic property of the substance, defined as the quotient of the substance's volume to its mass. It is the reciprocal of density ρ (rho) and it is also related to the molar volume and molar mass:
The Jeans instability is a concept in astrophysics that describes an instability that leads to the gravitational collapse of a cloud of gas or dust. It causes the collapse of interstellar gas clouds and subsequent star formation. It occurs when the internal gas pressure is not strong enough to prevent the gravitational collapse of a region filled with matter. It is named after James Jeans.
A reference atmospheric model describes how the ideal gas properties of an atmosphere change, primarily as a function of altitude, and sometimes also as a function of latitude, day of year, etc. A static atmospheric model has a more limited domain, excluding time. A standard atmosphere is defined by the World Meteorological Organization as "a hypothetical vertical distribution of atmospheric temperature, pressure and density which, by international agreement, is roughly representative of year-round, midlatitude conditions."
In atmospheric thermodynamics, the virtual temperature of a moist air parcel is the temperature at which a theoretical dry air parcel would have a total pressure and density equal to the moist parcel of air. The virtual temperature of unsaturated moist air is always greater than the absolute air temperature, however, as the existence of suspended cloud droplets reduces the virtual temperature.
Vertical pressure variation is the variation in pressure as a function of elevation. Depending on the fluid in question and the context being referred to, it may also vary significantly in dimensions perpendicular to elevation as well, and these variations have relevance in the context of pressure gradient force and its effects. However, the vertical variation is especially significant, as it results from the pull of gravity on the fluid; namely, for the same given fluid, a decrease in elevation within it corresponds to a taller column of fluid weighing down on that point.
