The correct answer to the given question is option B: hyperbolic expansion.

Explanation:
Expansion processes in thermodynamics are classified based on the relationship between pressure (P) and volume (V) during the process. The given relationship, pV = constant, represents a hyperbolic expansion process.

Let's understand the different types of expansion processes:

1. Parabolic Expansion: In a parabolic expansion process, the relationship between pressure and volume is given by pV^2 = constant. This type of expansion is not represented by the given equation pV = constant.

2. Hyperbolic Expansion: In a hyperbolic expansion process, the relationship between pressure and volume is given by pV = constant. This is the equation stated in the question, and it represents a hyperbolic expansion process.

3. Isentropic Expansion: An isentropic expansion process is characterized by constant entropy. The relationship between pressure and volume during an isentropic expansion process is not necessarily pV = constant. Therefore, option C is incorrect.

4. Adiabatic Expansion: An adiabatic expansion process is characterized by no heat transfer between the system and its surroundings. The relationship between pressure and volume during an adiabatic expansion process is given by pV^γ = constant, where γ is the ratio of specific heats. Therefore, option D is incorrect.

5. Free Expansion: A free expansion process occurs when a gas expands into a vacuum without any external work being done. In this case, the gas expands freely and the pressure and volume relationship is not defined by any specific equation. Therefore, option E is incorrect.

In conclusion, the correct answer is option B: hyperbolic expansion, as it represents the given equation pV = constant.