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 the falsely mystical view of art that assumes a kind of supernatural inspiration, a possession by universal forces unrelated to questions of power and privilege or the artist’s relation to bread and blood. In this view, the channel of art can only become clogged and misdirected by the artist’s concern with merely temporary and local disturbances. The song is higher than the struggle.”
—Adrienne Rich (b. 1929)