Ab initio total-energy calculations, based on the exact muffin-tin orbitals method, are used to determine the equilibrium chemical configuration of Pd_0.5Ag_0.5 alloy as a function of disorder and temperature. The transition from a substitutionally disordered face-centred-cubic crystallographic phase to an ordered L1₁ phase is monitored using the coherent potential approximation which allows us to continuously scan the order parameter and thermodynamics of the alloy. We find signs of a first-order phase transition from a substitutionally disordered state to a partially ordered state around 210 K temperature and the completely ordered L1₁ state is predicted around 90 K.