Bulk modulus
The bulk modulus (symbol: K) is an intense and substance Internal physical size of the theory of elasticity. It describes the all-round pressure change is necessary to produce a certain volume change (where no phase transition must occur). The property of materials that they offer resistance to compression, has its origin in the Pauli principle.
The compression, compression, compression is a ( all sides ) compressing a body, which reduces the volume and increases its density (mass density). Bodies are considered as compressible as the pressure changes occurring are sufficient to cause significant changes in density, which usually (only ) in the case of gases. After the operation, the body is compacted (compressed). In general, only an elastic deformation and densification occurs reversed when the pressure is back to, the body expands again ( expansion = expansion). Namely, in case of solids depends on the material at high pressures sometimes occur a permanent change in the structure with increased density, however, the permanent compression is another process that is not described by the compression module. An increase in other specific sizes as the mass density is not described by the compression module.
Definition
The compression modulus is defined as:
The negative sign arises because a pressure increase, the volume decreases thus dV is negative, but K should remain positive. The SI unit of the bulk modulus is Pascal or Newton / square meter. The compression module is a material constant that is dependent on the temperature and the pressure. The numerical value represents the pressure at which the volume to 0 when the compression modulus would not be increased at higher pressures.
The individual symbols stand for the following sizes:
- V - volume
- Dp - infinitesimal pressure change
- DV - infinitesimal volume change
- DV / V - relative volume change
Compressibility
The reciprocal of the bulk modulus is the compressibility (symbol: κ or χ ), and compressibility. This is often used in gas and liquid instead of the compression module.
We distinguish between isothermal compressibility (constant temperature and constant number of particles ), the free energy is
And adiabatic compressibility (constant entropy and constant number of particles ), the internal energy is
For gases, the compressibility follows in the context of approximation as ideal gas Boyle 's law with the simple result:
Wherein ( often referred to as κ ) the isentropic exponent is.
The compressibility of liquids has long been doubted until 1761, Jacob Perkins in 1820 and Hans Christian Oersted in 1822 were detected by measuring John Canton.
Bulk modulus of solids with isotropic material behavior
One can calculate the bulk modulus in this case from other elastic constants, assuming linear-elastic behavior and isotropic material:
Where:
- E - modulus of elasticity
- - Poisson's ratio
- G - shear modulus
Examples
Water
The compression modulus of water is 2.08 · 109 Pa at a temperature of 10 ° C under atmospheric pressure.
Taking into account the compressibility of water in the calculation of the pressure with one, arises with the compressibility of the following diagram:
At a density of 1000 kg / m³ at 0 m depth results from compressibility of water at a depth of 12,000 m, an increase of the density there by 6% to 1060 kg / m³ and thus an increase in the calculated real pressure from the ideal ( without density increase) of about 3.5 %. Here, however, the still prevailing in the sea influences of temperature, gas and salt contents are ignored.
Neutron stars
In neutron stars all atomic shells are under pressure from the gravitational collapse and the electrons have combined with protons of atomic nuclei to neutrons. Neutrons are inkompressibelste form of matter, which is known. Your bulk modulus is 20 orders of magnitude higher than that of diamond.