For the process to occur under adiabatic conditions, the correct condition is:
(i) Δ T=0
(ii) Δ p=0
(iii) q = 0
(iv) w = 0
A system is said to be under adiabatic conditions if there is no exchange of heat between the system and its surroundings. Hence, under adiabatic conditions, q = 0.
Therefore, alternative (iii) is correct.