The triangle-well (TW) potential is a simple model which is able to capture the essence of the intermolecular attraction in real molecules. Transition matrix Monte Carlo simulations in the grand canonical ensemble (GC-TMMC) are performed to investigate the role of the range of attraction on the features of fluid phase equilibria. As the TW potential range increases, the vapour-liquid coexistence curves shift towards a higher temperature range with the critical temperature and pressure increasing, and the critical density values decreasing. These GC-TMMC results are in excellent agreement with the predictions of Gibbs ensemble Monte Carlo and replica exchange Monte Carlo (REMC) simulations reported in literature. Using the GC-TMMC method, the vapour pressures are also computed directly from the particle number probability distributions (PNPDs). It has been noted in literature that the surface tension values are computationally more expensive and difficult to determine than other coexistence properties using molecular simulations. The PNPDs from GC-TMMC simulations along with Binder's formalism allow for the calculation of the interfacial tension with relative ease. Also, our simulation generated results for the interfacial tension are in good agreement with the literature data obtained using REMC (via the virial route) and the plots of our interfacial tension values as a function of temperature are smooth unlike the literature data. © 2016 Elsevier B.V. All rights reserved.