In this work, natural convection and entropy generation in a square cavity with an obstacle filled with Cu-water nanofluid is numerically studied. Horizontal walls of the cavity are adiabatic and vertical walls are maintained at a different constant temperature. The study has been done for the Rayleigh numbers between $10^3$ and $10^6$, the obstacle dimensions (W/L) of 0.1-0.5 and for base fluid as well as nanofluid. It is found that, using the nanofluid overall leads to increase the flow strength, Nusselt number and entropy generation and decrease the Bejan number especially at high Rayleigh numbers. It is observed that by increasing the obstacle dimensions, the entropy generation increases and the Bejan number decreases, but the effect of the obstacle dimensions on Nusselt number depends on Rayleigh number. For the present thermal system, the increasing Nusselt number compared to increasing entropy generation due to increase obstacle dimensions is significant at low Rayleigh numbers.