Climate models serve as critical tools for evaluating the effects of climate change and projecting future climate scenarios. However, the reliance on numerical simulations of physical equations renders them computationally intensive and inefficient. While deep learning methodologies have made significant progress in weather forecasting, they are still unstable for climate emulation tasks. Here, we propose PACE, a lightweight 684K parameter Physics Informed Uncertainty Aware Climate Emulator. PACE emulates temperature and precipitation stably for 86 years while only being trained on greenhouse gas emissions data. We incorporate a fundamental physical law of advection-diffusion in PACE accounting for boundary conditions and empirically estimating the diffusion co-efficient and flow velocities from emissions data. PACE has been trained on 15 climate models provided by ClimateSet outperforming baselines across most of the climate models and advancing a new state of the art in a climate diagnostic task.