Power consumption is likely to remain a significant concern for exascale performance in the foreseeable future. In addition, graphics processing units (GPUs) have become an accepted architectural feature for exascale computing due to their scalable performance and power efficiency. In a recent study, we found that we can achieve a reasonable amount of power and energy savings based on the selection of algorithms. In this research, we suggest that we can save more power and energy by varying the block size in the kernel configuration. We show that we may attain more savings by selecting the optimum block size while executing the workload. We investigated two kernels on NVIDIA Tesla K40 GPU, a Bitonic Mergesort and Vector Addition kernels, to study the effect of varying block sizes on GPU power and energy consumption. The study should offer insights for upcoming exascale systems in terms of power and energy efficiency.