acoustic wave equation
hamugeš-e mowj-e sedâyi
Fr.: équation de l'onde acoustique
A → differential equation that describes the time evolution of the → scalar potential of the field φ. It is expressed by: ∇2φ = (1/c2)∂2φ/∂t2, where c is → velocity of → longitudinal waves and ∇2 is the → Laplacian operator.
Fr.: équation algébrique
An equation in the form of P = 0, where P is a → polynomial having a finite number of terms.
Fr.: équation annuelle
An irregularity in the Moon's orbit, which can amount to 11 degrees in a period of one year. It results from the Sun's disturbing effect on the motion of the Moon due to varying distance between them.
Fr.: équation d'Antoine
A mathematical expression, derived from the → Clausius-Clapeyron equation, of the relation between the vapor pressure and the temperature of pure substances. It shows that the logarithm of vapor pressure is linearly dependent on the reciprocal of → absolute temperature.
Named after Louis Charles Antoine (1825-?), a French marine engineer, who derived the equation; → equation.
Fr.: équation d'Arrhenius
An important relationship in physical chemistry that combines the concepts of → activation energy and the → Maxwell-Boltzmann distribution law. It is expressed by: k = Ae-Ea/(RT), where k is the chemical → reaction rate, Ea is the activation energy, R is the → gas constant, and T is → temperature.
Named for Svante Arrhenius (1859-1927), Swedish chemist and physicist who suggested the relationship in 1889.
Fr.: équation de Bernoulli
The equation expressing → Bernoulli's theorem: P + (1/2)ρV2 + ρgz = constant, where P is the fluid → pressure, V is → velocity, ρ is → density, g is the acceleration due to → gravity, and z is the vertical reference → level. The theree terms are called → static pressure, → dynamic pressure, and → hydrostatic pressure, respectively. The Bernoulli equation states that the total pressure along a → streamline is → constant.
→ Bernoulli's theorem; → equation.
Fr.: équation de Bessel
A linear second-order differential equation, the solutions to which are called Bessel functions.
Hamugeš, → equation.
Fr.: équation de Boltzmann
1) An equation that expresses the relative number (per unit volume) of → excited atoms in different states as a function of the temperature for a gas in → thermal equilibrium: Nu/Nl = (gu/gl) exp (-ΔE/kTex), where Nu and Nl are the upper level and lower level populations respectively, gu and gl the → statistical weights, ΔE = hν the energy difference between the states, k is → Boltzmann's constant, and h → Planck's constant.
→ Boltzmann's constant; → equation.
Fr.: équation canonique
The most general form of an equation.
Fr.: équation de Cauchy
A relationship between the → refractive index (n) and the wavelength of light (λ) passing through a medium. It is commonly stated in the following form: n = A + B/λ2 + C/λ4, where A, B, and C are constants characterizing the medium. The two-component Cauchy equation is n = A + B/λ2, from which the dispersion becomes dn/dλ = -2B/λ3 showing that dispersion varies approximately as the inverse cube of the wavelength. The dispersion at 4000 A will be about 8 times as large as at 8000 Å.
Named after Augustin Louis Cauchy (1789-1857), French mathematician and physicist who found the first equation of dispersion in 1836; → equation.
Fr.: équation caractéristique
Physics: An analytical relationship between a set of physical
variables that determines the state of a physical system.
→ characteristic; → equation.
Fr.: équation chimique
The symbolic representation of a chemical reaction where the formulae of the → reactants are placed on the left and the formulae of → products on the right of an arrow.
Fr.: équation de Clapeyron
An equation that relates the temperature and pressure dependence of phases in equilibrium with the heat interaction and volume change associated with a phase change: dP/dT = L/T ΔV, where dP/dT is the slope of the coexistence curve, L is the → latent heat, T is the temperature, and ΔV is the volume change of the phase transition.
Named after Émile Clapeyron (1799-1864), a French engineer and physicist, one of the founders of → thermodynamics; → equation.
Fr.: équation de Clausius
A first-order improvement on the → ideal gas law that corrects for the finite volume of molecules.
Fr.: équation de Clausius-Clapeyron
An approximation of the → Clapeyron equation for liquid-vapor equilibrium that incorporates the → ideal gas law and states that the logarithm of vapor pressure is inversely proportional to temperature.
Fr.: équation de Compton
Theoretical equation which gives the change in the photon wavelength due to the → Compton effect.
cosmic energy equation
hamugeš-e kâruž-e keyhâni
Fr.: équation de l'énergie cosmique
Same as the → Layzer-Irvine equation.
Fr.: équation cubique
An equation containing unknowns of the third power; the general form: ax3 + bx2 + cx + d = 0.
de Broglie equation
hamugeš-e de Broglie
Fr.: équation de de Broglie
According to the → de Broglie hypothesis,
which has been verified by experiments, every → particle
of matter, whatever its nature, has a characteristic → wavelength
associated with its wavelike quantum aspect. The de Broglie equation gives the
equivalent wavelength of a moving particle: λ = h/mv, where h is
→ Planck's constant, m the mass of the particle,
and v its velocity.
Named after Louis Victor de Broglie (1892-1987), French physicist, creator of a new field in physics, wave mechanics, who won the Nobel prize in physics in 1929. → equation
Fr.: équation de Dieterici
An → equation of state for → real gases which leads to the → van der Waals equation as a → first approximation. It is of the form P(V - b) [exp (a/VRT)] = RT, where P is the pressure, V is the volume, T is the thermodynamic temperature, R is the → gas constant, and a and b are the constants characteristic of the gas.
Named after Conrad Dieterici (1858-1929), a German physicist; → equation.