  By dropping particles into black hole, we have employed the recently new
assumption [1] that the change of the black hole mass(enthalpy) should be the
same amount as the energy of an infalling particle($\omega = dM$), to carefully
test the laws of thermodynamics and the weak cosmic censorship conjecture of a
conformal anomaly corrected AdS black hole in different phase spaces. Using the
energy-momentum relation, the result shows that the first law, second law and
weak cosmic censorship conjecture of black hole are all valid in the normal
phase space, no violations occur. In the extended phase space, it firstly shows
that 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 phase
spaces. Also, it is true that there are always horizons by which the
singularity is also covered. So, the configurations of the extremal and
near-extremal black holes will not be changed, and there has no violation of
the weak cosmic censorship conjecture. Finally, all of those conclusions are
independent of the scalar curvature parameter $k$ and the conformal anomaly
parameter $\tilde{\alpha}$
