  In this paper we present a closed-form expression of the vibrational
partition function for the one-dimensional q-deformed Morse potential energy
model. Through this function the related thermodynamic functions are derived
and studied in terms of the parameters of the model. Specially, we plotted the
q-deformed vibrational partition function, and vibrational specific heat for
some diatomic molecule systems such as H2, HCl, LiH and CO. The idea of a
critical temperature T_{C} is introduced in relation to the specific heat.
