Let P = pressure, V = volume and T = Temperature of the gas in a cylinder fitted with a perfectly frictionless piston.
Suppose a small amount of heat d Q is given to the system. The heat is spent in two ways:-
1) In increasing the temperature of the gas by la small range d T, at constant volume 2) In expansion of gas by a small volume d v So, d Q = CV d T + P d V In adiabatic change, no heat is supplied from outside So, d Q = O