All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
We do not know what you mean by the method of operation of the refrigerator and air-conditioner from the verse which you mentioned. If you mean that this is a scientific sign, then you should know that, in principle, the Quran is a book of guidance and not a book of science. In addition to this, this science – meaning the scientific signs in the Quran and the Sunnah – has its conditions, and we mentioned some of them in Fataawa 89442 and 87767.
Therefore, if what you want to mention is based on true scientific foundations, and the interpretation of the texts of the Quran and the Sunnah is taken from the statements of the prominent scholars, then it is permissible for you to write this book and financially benefit from it. However, before you publish it, you should present it to some authorities which are specialized in the matter of scientific signs (of the Quran), like the Commission on Scientific Signs of Quran and Sunnah.
Allaah Knows best.