Thermodynamic Relation
Strictly speaking, the bulk modulus is a thermodynamic quantity, and in order to specify a bulk modulus it is necessary to specify how the temperature varies during compression: constant-temperature (isothermal ), constant-entropy (adiabatic ), and other variations are possible. Such distinctions are especially relevant for gases.
For an ideal gas, the adiabatic bulk modulus is given by
and the isothermal bulk modulus is given by
where
- γ is the adiabatic index, sometimes called κ.
- P is the pressure.
When the gas is not ideal, these equations give only an approximation of the bulk modulus. In a fluid, the bulk modulus K and the density ρ determine the speed of sound c (pressure waves), according to the Newton-Laplace formula
In solids, and have very similar values. Solids can also sustain transverse waves: for these materials one additional elastic modulus, for example the shear modulus, is needed to determine wave speeds.
Read more about this topic: Bulk Modulus
Famous quotes containing the word relation:
“There is undoubtedly something religious about it: everyone believes that they are special, that they are chosen, that they have a special relation with fate. Here is the test: you turn over card after card to see in which way that is true. If you can defy the odds, you may be saved. And when you are cleaned out, the last penny gone, you are enlightened at last, free perhaps, exhilarated like an ascetic by the falling away of the material world.”
—Andrei Codrescu (b. 1947)