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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 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 ...
−9.04 × 10 −6 volume SI units [7] Thermodynamic properties ... γ – Thermal expansion coefficient as 10 −3 per kelvin; ... Water/steam data table at triple ...
Negative thermal expansion (NTE) is an unusual physicochemical process in which some materials contract upon heating, rather than expand as most other materials do. The most well-known material with NTE is water at 0 to 3.98 °C. Also, the density of solid water (ice) is lower than the density of liquid water at standard pressure.
The low compressibility of water means that even in the deep oceans at 4 kilometres (2.5 mi) depth, where pressures are 40 MPa, there is only a 1.8% decrease in volume. [43] The bulk modulus of water ice ranges from 11.3 GPa at 0 K up to 8.6 GPa at 273 K. [44] The large change in the compressibility of ice as a function of temperature is the ...
Note that the especially high molar values, as for paraffin, gasoline, water and ammonia, result from calculating specific heats in terms of moles of molecules. If specific heat is expressed per mole of atoms for these substances, none of the constant-volume values exceed, to any large extent, the theoretical Dulong–Petit limit of 25 J⋅mol ...
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):
Some formulations for the Grüneisen parameter include: = = = = = ( ) where V is volume, and are the principal (i.e. per-mass) heat capacities at constant pressure and volume, E is energy, S is entropy, α is the volume thermal expansion coefficient, and are the adiabatic and isothermal bulk moduli, is the speed of sound in the medium ...