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# Analyzing a Simple Cycle Using a $pV$ Curve

**Keywords:**Energy and Entropy, Work, Internal Energy, Small Group Activity, Ideal Gas

### Highlights of the activity

- This small group activity is designed to help upper division undergraduate students understand thermodynamic cycles for an ideal gas.
- Students use the ideal gas equation of state to work out the efficiency of the cycle.
- The wrap-up discussion contrasts the efficiency of this cycle with the Carnot efficiency.

### Reasons to spend class time on the activity

At this point in the course, students have acquired a large amount of experience in relating thermal partial differentials using Legendre Transforms to find Maxwell's relations; furthermore, much of these lessons place emphasis on important thermodynamic theory. This activity provides a solid mathematical exercise. Each group will explicitly calculate the change in work, heat, and energy in a thermodynamic process. The students will have to analyze the information given in the problem to find the information necessary to solving the problem. Also, groups will have the opportunity to use the first law of thermodynamics and the thermodynamic identity to find the integral necessary for solving the heat and work on each leg.