During adiabatic process pressure P versus density ρ equation is:
Pργ= constant
Pρ-γ = constant
Pγρ1+γ = constant
P1γργ = constant
In adiabatic process,
PVγ = constant-------(1)
Density ρ = mV
or ρ ∞ V-1
Hence equation(1) can be written as
pρ-γ = constant