| With this Mathcad 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. Pressure versus volume is integrated using the trapezoid rule, and compared to exact calculations.
A much more challenging problem is to repeat the calculation, using 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.
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Figure 1. The shaded area represents the work done on the gas during expansion. It is calculated numerically using "the trapezoid rule".
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