## Physics Friday 75

Previously, I discussed the heat capacity ratio, also called the adiabatic index, γ, and derived the adiabatic condition, PVγ=const. Now, let us consider what happens to the temperature when an ideal gas changes volume via an adiabatic process. Solving the ideal gas law for pressure, we get . Substituting this into the adiabatic condition, we see that



As γ>1, γ-1>0, and so the temperature decreases when the gas expands adiabatically, and increases when the gas is compressed; these are known as adiabatic cooling and adiabatic heating, respectively.