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Based on the new version of the gedanken experiment proposed by Sorce andWald, we investigate the weak cosmic censorship conjecture (WCCC) for aReissner-Nordstr\"{o}m-Anti-de Sitter (RN-AdS) black hole under theperturbation of extra matter fields. Firstly, we propose that the cosmologicalconstant can be effectively derived from the matter fields and its value varieswith the matter fields perturbing the black hole. Meanwhile, we assume that theperturbation satisfies the stability condition. This condition means that aftera long time of the perturbation, the black hole solution also belongs to thefamily of the RN-AdS solution. After that, based on both the stabilitycondition and the null energy condition, while using the off-shell variationmethod, the first-order and the second-order perturbation inequalities arederived respectively when the cosmological constant is considered as a dynamicvariable. It is the first time to extend the two perturbation inequalities tocontain the term of the press and volume of thermodynamics. Finally, we performthe two perturbation inequalities into testing the WCCC for the RN-AdS blackhole under the second-order approximation of the perturbation. It is shown thatif 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, theWCCC for the RN-AdS black hole is valid under the second-order approximation ofthe perturbation.

Examining the weak cosmic censorship conjecture of RN-AdS black holes via the new version of the gedanken experiment