In the study of pneumatics, it is inevitable to refer to the basic laws of thermodynamics. In the past, a number of engineering authors often wrote heat Q and the micro-increments of the work done by the gas W as dQ and dW, which are, however, not correct expressions as far as a strict mathematical theory is concerned. When participating in the editing of the Aviation Air Force Manual, the author raised this issue. In the second edition of the manual, dQ and dW were corrected to δW and δQ. But some pneumatic works still fail to pay attention to the problem, and are still used to using dQ and dW. In this article, a rigorous proof is conducted and the concept of the thermodynamic space is proposed to clarify the confusion in the past.