  Based on the new version of the gedanken experiment proposed by Sorce and
Wald, we investigate the weak cosmic censorship conjecture (WCCC) for a
Reissner-Nordstr\"{o}m-Anti-de Sitter (RN-AdS) black hole under the
perturbation of extra matter fields. Firstly, we propose that the cosmological
constant can be effectively derived from the matter fields and its value varies
with the matter fields perturbing the black hole. Meanwhile, we assume that the
perturbation satisfies the stability condition. This condition means that after
a long time of the perturbation, the black hole solution also belongs to the
family of the RN-AdS solution. After that, based on both the stability
condition and the null energy condition, while using the off-shell variation
method, the first-order and the second-order perturbation inequalities are
derived respectively when the cosmological constant is considered as a dynamic
variable. It is the first time to extend the two perturbation inequalities to
contain the term of the press and volume of thermodynamics. Finally, we perform
the two perturbation inequalities into testing the WCCC for the RN-AdS black
hole under the second-order approximation of the perturbation. It is shown that
if the variation of the cosmological constant is caused by the matter fields,
while the stability condition and the null energy condition are all satisfied,
the black hole cannot be destroyed after the perturbation. In other words, the
WCCC for the RN-AdS black hole is valid under the second-order approximation of
the perturbation.
