Adiabatic process is isentropic but i can't get it why is it so. If we go by statistical method S=KlnW(where W is the thermodynamic probability), so if we look into adiabatic expansion the volume increases so we can say that the thermodynamic probability increases and hence the entropy of the system should increase. Moreover, if we look into isothermal expansion of an ideal gas in vaccum there would be no work done and so no heat would enter or move out of the system but since there is a change in volume we can write ∆S=nRln(V2/V1).

Adiabatic process is isentropic, but I can't get it why is it so. If we go by statistical method

$$S = K\ln W,$$

where $W$ is the thermodynamic probability, and if we look into adiabatic expansion the volume increases, we can say that the thermodynamic probability increases, and hence the entropy of the system should increase. 

Moreover, if we look into isothermal expansion of an ideal gas in vacuum, there would be no work done, and so no heat would enter or move out of the system. But since there is a change in volume, we can write

$$∆S = nR\ln\frac{V_2}{V_1}.$$