Evaluating the Efficiency of the Carnot Cycle with a van der Waals Gas

The efficiency of a perfect heat engine running with an ideal gas operating between two heat reservoirs is optimized by Sadi Carnot. It is known that the efficiency is independent of the working body and depends on the temperatures of the two heat reservoirs only. The detail of the proof, however, in most of the approaches relies implicitly on the assumption that the gas is ideal. The author revisits the concept and has generalized the proof assuming the working body to obey the nonideal gas law. Pedagogically, with this realistic explicit model it is shown that the efficiency of the cycle stays intact. Mathematica's symbolic calculation power is deployed throughout the work. A Mathematica package is crafted to automate and evaluate the efficiency of the cycle. This package can prove useful in teaching thermo physics and engineering college courses.