A formal physical cluster theory for an imperfect gas, valid for an arbitrary definition of a "physical cluster", is described. The role of the definition of the physical cluster is stressed. For a particular definition of the physical cluster, which may be appropriate in nucleation theory, the Helmholtz free energy of 13-, 43-, 60-, 70-, 80-, 87-, and 100-atom argon clusters is calculated in the classical limit for temperatures ranging from absolute zero to 100°K using Monte Carlo techniques. It is found that a cluster's free energy is almost independent of its definition provided that the definition is reasonable and the temperature is sufficiently low. The results are compared with the predictions using the harmonic approximation.