The adiabatic index of a gas, usually denoted by the symbol κ (kappa) (also called γ), is the ratio of its specific heat at constant pressure (c_p) to its specific heat at constant volume (c_V).

κ = c_p/c_V

One can easily understand the relation if one thinks of the following experiment: A cylinder closed at one end with a blocked piston is filled with air.   This cylinder is then heated.   Since the piston cannot move the volume is constant.   Temperature and pressure will rise.   One stops the heating noting how much energy one has added to the system (c_v) and frees the piston.   The piston will move outward and by adiabatic expansion, the gas cools.   To bring the temperature of the gas to its former level one has to heat it a little bit.   This extra heat amounts to about 40% of c_v thus:

c_p = 1.402 · c_V

A value often used in aerodynamics is

c_p - c_V = 0.4

Kappa can also refer to several other things, but it can usually be determined by the context which one. Sometimes the Greek letter gamma γ is used.