Students should be familiar with the basic definitions of pressure, volume, temperature, and internal energy.
Goals:
- Equation and definition of an Ideal Gas
- Students explore what it would mean for something to be an ideal gas or a good approximation of an ideal gas
- Students might discuss the difference between temperature and internal energy
- Can discuss degrees of freedom
Time Estimate: 30 minutes + 10 minutes whole class discussion
Tools and Equipment:
- Purple and Blue Thermo surfaces for each group
- Remote Option: Ideal Gas Contour Maps
- Student handout for each student
- A personal or shared writing space for each student to write/draw/sketch
Intro:
- Students should be familiar with the basic definitions of pressure, volume, temperature, and internal energy
Whole Class Discussion:
- A whole class discussion should eleicit student ideas about how to determine if a system fits the ideal gas model perfectly, and when the ideal gas moadel is a “good" fit.
The internal energy of a triatomic ideal gas is described by the equation:
\[ U(p,T)=\left(\frac{\# dof}{2}\right) NkT \]
The contours map presents the internal energy of water vapor: it shows volume and internal energy contours plotted on temperature and pressure axes.
By examining the plastic surfaces, how can you tell if an ideal gas model is a good model for water vapor?
Solution: The biggest indicator on the p-T graph is if the internal energy contours are nearly parallel to the volume axis (constant at constant temperature) AND they have the same, constant spacing between them. Also, volume contours are nearly linear (ideal gas law). For an ideal gas on the S-V graph, isotherms should be parallel to and never cross the U contours, i.e. on the purple surface the isotherms are level curves.
Hint: Students might benefit from sketching a graph of internal energy vs.temperature for an ideal gas, then sketching a plot of internal energy vs.temperature for water vapor, using the values from the contour map.
WCD: The instructor might model the blue surface, describing the features of the surface, including its near-flatness. (Although it is not a perfectly flat, and this can be modeled by placing the surface upside down on a flat table, against a small whiteboard, etc.)
WCD: One can discuss degrees of freedom and gasses/situations that are typically modeled as ideal.