For each measured quantum coherent trajectory, we separately identify energy changes of the qubit as heat and work, and verify the first law of thermodynamics for an open quantum system. We further employ a novel quantum feedback loop to compensate for the exchanged heat and effectively isolate the qubit. By verifying the Jarzynski equality for the distribution of applied work, we demonstrate the validity of the second law of thermodynamics. Our results establish thermodynamics along individual quantum trajectories.