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The volumetric thermal expansion coefficient is the most basic thermal expansion coefficient, and the most relevant for fluids. In general, substances expand or contract when their temperature changes, with expansion or contraction occurring in all directions. Substances that expand at the same rate in every direction are called isotropic. For ...
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 ...
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 ...
1 Thermal expansion. 2 Notes. 3 References. Toggle References subsection. 3.1 CRC. 3.2 CR2. 3.3 LNG. 3.4 WEL. Toggle the table of contents. Thermal expansivities of ...
β is the coefficient of volume expansion (equal to approximately 1/T for ideal gases) T s is the surface temperature; T ∞ is the bulk temperature; L is the vertical length; D is the diameter; ν is the kinematic viscosity. The L and D subscripts indicate the length scale basis for the Grashof number.
We assume the expansion occurs without exchange of heat (adiabatic expansion). Doing this work, air inside the cylinder will cool to below the target temperature. To return to the target temperature (still with a free piston), the air must be heated, but is no longer under constant volume, since the piston is free to move as the gas is reheated.
This provides an expression for the Joule–Thomson coefficient in terms of the commonly available properties heat capacity, molar volume, and thermal expansion coefficient. It shows that the Joule–Thomson inversion temperature, at which μ J T {\displaystyle \mu _{\mathrm {JT} }} is zero, occurs when the coefficient of thermal expansion is ...