Of course, but I am busy now. I will only be able to do it during the Christmas holidays. Anyway, I don't believe at all that we can guarantee that the internal energy does not change in a reversible transformation: as you also said, you would have to do work from outside. I wouldn't know how to deal with reversible transformation calculations at all. Nor even with irreversible transformation. I'm beginning to think that the simplest approximation is the application of the perfect gas law.
Thank you very much for your intelligent answers.