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By dropping particles into black hole, we have employed the recently newassumption [1] that the change of the black hole mass(enthalpy) should be thesame amount as the energy of an infalling particle($\omega = dM$), to carefullytest the laws of thermodynamics and the weak cosmic censorship conjecture of aconformal anomaly corrected AdS black hole in different phase spaces. Using theenergy-momentum relation, the result shows that the first law, second law andweak cosmic censorship conjecture of black hole are all valid in the normalphase space, no violations occur. In the extended phase space, it firstly showsthat the first law of black hole thermodynamics is always true in our case.Then, we interestingly find that if the condition ${d\ell} > -\left(P^r\ell^3\right)/{r_+^3}$ satisfied the variation of entropy is always positive,which means there would be no violation of the second law in the extend phasespaces. Also, it is true that there are always horizons by which thesingularity is also covered. So, the configurations of the extremal andnear-extremal black holes will not be changed, and there has no violation ofthe weak cosmic censorship conjecture. Finally, all of those conclusions areindependent of the scalar curvature parameter $k$ and the conformal anomalyparameter $\tilde{\alpha}$

Testing thermodynamic laws and weak cosmic censorship conjecture of conformal anomaly corrected AdS black hole