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A number of materials contract on heating within certain temperature ranges; this is usually called negative thermal expansion, rather than "thermal contraction".For example, the coefficient of thermal expansion of water drops to zero as it is cooled to 3.983 °C (39.169 °F) and then becomes negative below this temperature; this means that water has a maximum density at this temperature, and ...
where α is the coefficient of thermal expansion. [ 2 ] : 128–129 The Boussinesq approximation states that the density variation is only important in the buoyancy term. If F = ρ g {\displaystyle F=\rho \mathbf {g} } is the gravitational body force, the resulting conservation equation is [ 2 ] : 129
β is the thermal expansion coefficient (equals to 1/T, for ideal gases, where T is absolute temperature). is the kinematic viscosity; α is the thermal diffusivity; T s is the surface temperature; T ∞ is the quiescent temperature (fluid temperature far from the surface of the object) Gr x is the Grashof number for characteristic length x
The laws of thermodynamics imply the following relations between these two heat capacities (Gaskell 2003:23): = = Here is the thermal expansion coefficient: = is the isothermal compressibility (the inverse of the bulk modulus):
This form of the ideal gas law is very useful because it links pressure, density, and temperature in a unique formula independent of the quantity of the considered gas. Alternatively, the law may be written in terms of the specific volume v, the reciprocal of density, as. It is common, especially in engineering and meteorological applications ...
In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure (CP) to heat capacity at constant volume (CV). It is sometimes also known as the isentropic expansion factor and is denoted by γ (gamma ...
where γ is the heat capacity ratio, α is the volumetric coefficient of thermal expansion, ρ = N/V is the particle density, and = (/) is the thermal pressure coefficient. In an extensive thermodynamic system, the application of statistical mechanics shows that the isothermal compressibility is also related to the relative size of fluctuations ...
Thermodynamics. In thermodynamics, the compressibility factor (Z), also known as the compression factor or the gas deviation factor, describes the deviation of a real gas from ideal gas behaviour. It is simply defined as the ratio of the molar volume of a gas to the molar volume of an ideal gas at the same temperature and pressure.