Show that Laplace correction for elasticity of gaseous medium is E = gamma p, where 'gamma' is the ratio of specific heates.

Show that Laplace correction for elasticity of gaseous medium is E = g

1.	Show that Laplace correction for elasticity of gaseous medium is E = gamma p, where 'gamma' is the ratio of specific heates.
Answer» Solution :Consider adiabatic variation in the PRESSURE and volume of gasesousmedium. `PV^(gamma) =0 ` i.e., `gamma PV^(gamma-1) Dleta V + V^(gamma) Delta P = 0` i.e., Bulk modulus-`( Delta P )/((DeltaV)/( V)) = gamma P` Hence in the expression`v = sqrt((E )/(rho ))`, Elasticity 'E' is replaced by `gamma P`. LAPLACE equation is written as `v =sqrt((gamma P )/( rho ))` Where `gamma = 1+ 2 //f` and'f' is number of degrees of freedom of gaseous molecule.