used rather than one based on this approximation, where possible. A rigorous value for the ratio can also be calculated by determining from the residual properties expressed as Values for are readily available and recorded, but values for need to be determined via relations such as these. See relations between specific heats for the derivation of the thermodynamic relations between the heat capacities. The above definition is the approach used to develop rigorous expressions from equations of state (such as Peng–Robinson), which match experimental values so closely that there is little need to develop a database of ratios or values. Values can also be determined through finite-difference approximation. Adiabatic process This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: is constant Using the ideal gas law, : is constant is constant where is the pressure of the gas, is the volume, and is the thermodynamic temperature. In gas dynamics we are interested in the local relations between pressure, density and temperature, rather than considering a fixed quantity of gas. By considering the density as the inverse of the volume for a unit mass, we can take in these relations. Since for constant entropy, , we have , or , it follows that For an imperfect or non-ideal gas, Chandrasekhar defined three different adiabatic indices so that the adiabatic relations can be written in the same form as above; these are used in the theory of stellar structure: All of these are equal to in the case of an ideal gas. See also Relations between heat capacities Heat capacity Specific heat capacity Speed of sound Thermodynamic equations Thermodynamics Volumetric heat capacity References Notes Thermodynamic properties Physical quantities Ratios Thought experiments in physics