We study one-dimensional diffusion of N hard-core interacting Brownian particles driven by the space- and time-dependent external force. We give the exact solution of the N-particle Smoluchowski diffusion equation. In particular, we investigate the nonequilibrium energetics of two interacting particles under the time-periodic driving. The hard-core interaction induces entropic repulsion which differentiates the energetics of the two particles. We present exact time-asymptotic results which describe the mean energy, the accepted work and heat, and the entropy production of interacting particles, and we contrast these quantities against the corresponding ones for the noninteracting particles.