Fluid transport through nanoporous membranes is subject to additional resistance at the membrane interface, a large part of which is due to the difference in thermodynamic states of the fluid inside and outside the membrane. The state of the fluid confined within a membrane depends on the size of the nanopores, which results in a corresponding dependence of the interfacial resistance. We investigate here the dependence of the thermodynamic resistance on the radius of the nanopore and the thickness of the pore wall, considering the transport of carbon dioxide and methane through carbon nanotubes of radii between 4 A and 50 A at room temperature, and a wide range of pressures. We find that the thermodynamic resistance strongly depends on the state of the fluid adsorbed in the membrane, which is determined by the size of the pores and the external pressure. In particular, for narrow micropores the thermodynamic resistance has two pressure regimes, being constant at low pressures and increasing gradually at high pressures. Furthermore, moderate and wide pores allow presence of multiple fluid phases with distinct condensation. In the corresponding pressure range the thermodynamic resistance is subjected to large fluctuations, which are not observed for small pores. Furthermore, our results reveal strong dependence of the thermodynamic resistance on the pore radius for very narrow pores and large pressures, when the state of the fluid inside of the membrane is most different from that of the external bulk fluid, with the resistance increasing with decrease in pore radius. Our results also indicate that analyzing the pore size dependence of the interfacial resistance makes it possible to distinguish the contribution of the thermodynamic resistance from the other sources of resistance to fluid flow through the membrane, in particular, the hydrodynamic resistance and the internal resistance.