The Carnot Cycle©
Harold H. Harris
Chemistry Department
University of Missouri-St. Louis
Saint Louis, MO 63121
United States
mail to: hharris@umsl.edu

In this document students investigate the Carnot cycle with numerical calculations on an ideal, monatomic gas. They discover the consequences on the net work and the thermodynamic efficiency of changing variables such as the pressure to which expansion occurs, and the working temperatures of the process. Especially informative are indicator diagrams in color, that illustrate the work associated with each step of the cycle (color indicator diagrams are not available when using Mathcad6). Pressure versus volume is integrated using the trapezoid rule, and compared to exact calculations.

A much more challenging problem is to repeat the calculation, except for a real gas equation of state. The van der Waals model of methane is thoroughly illustrated as an example; the instructor can decide how much of this help would be provided to students. Student groups might be assigned different gases or different equations of state, with as much of the van der Waals development provided as is appropriate for the course and the students.

The different levels of difficulty in the document are presented as columns in the document. In the first column of pages the calculations are developed for the ideal, monoatomic gas. The second column of pages contains the van der Waals equation implementation. The third column of document contains derivations of equations that are needed for the calculations involving nonideal gases.
Editor's Commentary
Audiences: Upper-Division Undergraduate
Pedagogies: Computer-Based Learning
Domains: Physical Chemistry
Topics: Mathematics / Symbolic Mathematics, Thermodynamics, Gases
File NameDescriptionSoftware TypeSoftware Version
CarnotVDW8.mcd JCE Mathcad 8 Computational Document Mathcad 8
CarnotVDW6.mcd JCE Mathcad 6 Computational Document Mathcad 6
CarnotVDWA.nb JCE Mathematica Computational Document Mathematica
CarnotVDWB.nb JCE Mathematica Computational Document Mathematica
CarnotVDW.pdf Read-Only Document from Mathcad 2000.
CarnotVDWA_nb.pdf Read-Only Document from Mathematica.
CarnotVDWB_nb.pdf Read-Only Document from Mathematica.
CarnotVDW2000.mcd JCE Mathcad 2000 Computational Document Mathcad 2000
JCE JCE Subscribers only: name and password or institutional IP number access required.
Harris, H. H. J. Chem. Educ. 2001, 78, 1556.
Comments to: Hal Harris at hharris@umsl.edu.
©Copyright 2001 Journal of Chemical Education