To determine whether an adiabatic process is polytropic, we need to understand the definitions of both terms.
An adiabatic process is one in which no heat is exchanged with the surroundings. This means that all the energy transfer occurs in the form of work done on or by the system.
A polytropic process, on the other hand, is defined by the relationship between pressure and volume, expressed as PV^n = constant, where n is the polytropic index. The value of n can take various forms depending on the nature of the process.
In fact, an adiabatic process is a specific case of a polytropic process where the polytropic index n equals the specific heat ratio (k) of the gas. Therefore, while all adiabatic processes are polytropic (with n set to k), not all polytropic processes are adiabatic.
In summary, yes, an adiabatic process is indeed a polytropic process, but it is characterized by a specific value of the polytropic index.