During adiabatic process, there is no transfer of heat into or out of a system i.e. ∆Q = 0.

Adiabatic conditions refer to a process in which there is no heat transfer between the system and its surroundings. In other words, the process occurs in isolation, and there is no exchange of heat energy. To determine the correct condition for a process to occur under adiabatic conditions, we need to consider the different variables associated with the process.

1. Definition of adiabatic process:
- An adiabatic process is defined as a process in which there is no heat transfer between the system and its surroundings.
- In an adiabatic process, the change in internal energy (ΔU) of the system is equal to the work done (W) on or by the system, i.e., ΔU = W.

2. Adiabatic condition:
- The correct condition for a process to occur under adiabatic conditions is when the heat transfer (q) is zero.
- This means that there is no heat exchange between the system and its surroundings.
- Mathematically, q = 0.

3. Explanation of other options:
a) p = 0: This condition refers to zero pressure. However, adiabatic conditions do not necessarily require zero pressure. The pressure can be any value as long as there is no heat transfer.
b) T = 0: This condition refers to absolute zero temperature. Adiabatic conditions do not necessarily require zero temperature. The temperature can be any value as long as there is no heat transfer.
d) w = 0: This condition refers to zero work done. Adiabatic conditions do not necessarily require zero work done. Work can be done on or by the system as long as there is no heat transfer.

4. Importance of adiabatic conditions:
- Adiabatic processes are of great importance in thermodynamics and engineering.
- They are commonly used in the analysis of various systems, such as gas turbines, compressors, and engines.
- Adiabatic processes allow for the study of energy conversion and efficiency without the complication of heat transfer.

In conclusion, the correct condition for a process to occur under adiabatic conditions is when there is no heat transfer (q = 0) between the system and its surroundings. This condition allows for the study and analysis of processes without the influence of heat exchange.