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With the Hamilton-Jacobi equation, we obtain the energy-momentum relation ofa charged particle as it is absorbed by the Gauss-Bonnet AdS black hole. On thebasis of the energy-momentum relation at the event horizon, we investigate thefirst law, second law, and weak cosmic censorship conjecture in both the normalphase space and extended phase space. Our results show that the first law,second law as well as the weak cosmic censorship conjecture are valid in thenormal phase space for all the initial states are black holes. However, in theextended phase space, the second law is violated for the extremal andnear-extremal black holes, and the weak cosmic censorship conjecture isviolable for the near-extremal black hole, though the first law is still valid.In addition, in both the the normal and extended phase spaces, we find theabsorbed particle changes the configuration of the near-extremal black hole,while don't change that of the extremal black hole.

Weak cosmic censorship conjecture with pressure and volume in the Gauss-Bonnet AdS black hole