![]() Differentiating with respect to the density, the equation becomes Taking the natural logarithm of both sides yields ln p − γ ln ρ = constant. The number of moles and the molar mass are constant and can be absorbed into the constant p ( 1 ρ ) γ = constant. The density equals the number of moles times the molar mass divided by the volume, so the volume is equal to V = n M ρ. Adiabatic processes are covered in detail in The First Law of Thermodynamics, but for now it is sufficient to say that for an adiabatic process, p V γ = constant, p V γ = constant, where p is the pressure, V is the volume, and gamma ( γ ) ( γ ) is a constant that depends on the gas. ![]() A process where heat is not added or removed from the system is known as an adiabatic system. During the process of compression and expansion of the gas, no heat is added or removed from the system. Ĭonsider a sound wave moving through air. ρ v d v = − d p ( − v d ρ ) v = − d p v = d p d ρ. Ρ v d v = − d p ( − v d ρ ) v = − d p v = d p d ρ.
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