Landau derivative
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In gas dynamics, the Landau derivative or fundamental derivative of gas dynamics, named after Lev Landau who introduced it in 1942,[1][2] refers to a dimensionless physical quantity characterizing the curvature of the isentrope drawn on the specific volume versus pressure plane. Specifically, the Landau derivative is a second derivative of specific volume with respect to pressure. The derivative is denoted commonly using the symbol or and is defined by[3][4][5]
where
is the sound speed; | |
is the specific volume; | |
is the density; | |
is the pressure; | |
is the specific entropy. |
Alternate representations of include
For most common gases, , whereas abnormal substances such as the BZT fluids exhibit . In an isentropic process, the sound speed increases with pressure when ; this is the case for ideal gases. Specifically for polytropic gases (ideal gas with constant specific heats), the Landau derivative is a constant and given by
where is the specific heat ratio. Some non-ideal gases falls in the range , for which the sound speed decreases with pressure during an isentropic transformation.