We present the thermoelastic properties of the body-centered cubic tantalum calculated within the quasi-harmonic approximation (QHA) and compare them with those given by the quasi-static approximation (QSA) and those measured experimentally. We find that the QHA temperature dependent elastic constants (TDECs) follow the experiment very well from 5 K up to 500 K, and in this range of temperatures are in better agreement with the experiment than the QSA TDECs. At higher temperatures, our QHA results are linear with temperature and fail to follow the measured change in slope of C(T) and C 44(T) that become parallel to the QSA results. We also present our QHA pressure dependent elastic constants at 5, 300, 1000, and 1500 K.
