The process in which change in pressure and volume and temperature takes place without any heat entering or leaving the system is called adiabatic change.
Consider some gas contained in an insulating barrel fitted with an air tight piston. On compressing the gas, heat is liberated. This liberated heat cannot move out due to the insulation of the barrel, resulting in a rise of temperature. On expanding the gas, heat is absorbed. This results in a fall of temperature. P-V diagram for an adiabatic change is shown in below figure.
It may be noted that the total heat of the system, undergoing an adiabatic change always remains constant.
The equation of state for adiabatic change is given by,
PV^{gamma } = Constant
Where ‘gamma’ is the ratio between the two specific heats of the gas.
gamma = frac{C_{p}}{C_{v}}
Here Cp and Cv are the molar specific heat capacities of the gas at constant pressure and at constant volume respectively.
For the diatomic gases at medium temperatures (250 K to 750 K), ‘gamma’ has a value of 1.42.