I was assigned a problem that stated pressure, p, and density, ρ, are related by the equation dp = -gρ dy. It said it follow the adiabatic equation p=p0(ρ/ρ0)^γ, where γ is not equal to 0, and p0 is pressure at earths surface and ρ0 is density at earths surface. It then wants me to show that
p = p0(1-((γ-1)/γ)*((ρ0gy)/p0))^(γ/(γ-1))
I've tried for an hour or more, and cannot figure out this problem. If anyone has any insight or even knows where to start, it would be greatly appreciated.