Calculating Expansion Work (using SymPy)

Expansion work is a key concept in chemical thermodynamics. In order to calculate expansion work, we must compute the definite integral of the equation of state that describes the expansion. Often, this is as simple as integrating the ideal gas law, but the same general steps apply to any equation of state.

This exercise first walks students through tools for performing integration using the SymPy package in Python. Next, students are asked to calculate the expansion work done by real and ideal gases, and compare the results to their expectations.

The SymPy tutorial is available on GitHub, the assignment prompt is available as a PDF, and the assignment is intended to be completed using a Jupyter Notebook. A key is available to instructors who email ajschoef@loyno.com from their institutional email address.

Calculating Expansion Work Using Python

Prerequisites

This activity assumes that students have familiarity with the following:

basic operations in Python (such as through the Python for Chemists tutorial)
differentiation and integration
the ideal gas law
real gas laws, such as the van der Waals equation of state and the virial equation of state
expansion work

Step 1

In order to perform integration using Python, students first need to understand a handful of commands in SymPy (Symbolic Python). The following set of Jupyter Notebooks will walk through these commands.

How to Use SymPy for Physical Chemists

Step 2

This PDF contains a detailed assignment prompt.