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Lecture 2 | State Variables & Equations of State, Ideal Gas

Microscopic Model of Gases

Lecture 2 | State Variables & Equations of State, Ideal Gas

Microscopic Model of Gases

The ideal gas law is a model that explains the observed relationships between thermodynamic quantities, such as temperature and pressure, of a lot of different gases. It was discovered experimentally, which is why it's called a law. For a gas to behave ideally, the particles the gas is comprised of must not interact, meaning they do not run into each other. This means that not all gases behave ideally and there is a degree to how ideal a gas is.

Thermodynamic state variables characterize the state of a thermodynamic system. The ideal gas law is a(n emperically derived) relationship between these variables.

This introduction to the ideal gas law from crash course chemistry is a great video to start this section.

Pre-lecture Study Resources

Watch the pre-lecture videos and read through the OpenStax text before doing the pre-lecture homework or attending class.

Thermodynamics | Ideal Gas Law

The Ideal Gas Law was first understand empirically through experimentation. It relates the thermodynamic state variables of temperature (T), pressure (P), volume (V), and number of particles (N). Since it is an equation comprised of variables that describe the state of the system, it is call an equation of state. Theoretically if a gas is truly ideal, that means the particles in the gas do not interact. There are other equations of state for gases that do not behave ideally. The ideal gas equation in physics is typically written as follows.

$PV=Nk_B T$, where kB is Boltzman's constant

Alternatively there is a form more typically seen in chemistry of $PV=nRT$. Here n represents the number of moles of particles in the gas and R is the Rydberg constant. Either form is valid and which one you use depends on what information is given. Either Way, since they are equivalent forms, then that must mean that $Nk_B = nR$, a useful relationship in other topics of thermo such as the kinetic theory of gases.

The graph is a 3D depiction of the ideal gas relationship with projections onto 2D surfaces.

This is a representation of how pressure, volume and temperature of a particle can be graphed on a single three dimensional graph. There is a pressure over temperature graph that is linear because of the equation the final pressure is equal to the initial pressure multiplied by the final temperature divided by the initial temperature. There is a pressure over volume graph which shows a curved graph because of the equation the final pressure is equal to the initial pressure multiplied by the initial volume divided by the final volume. There is a volume over temperature graph that has a linear relationship because of the equation the final volume is equal to the initial volume multiplied by the final temperature divided by the initial temperature.

*Graphic by Hyperphysics

Key Equations and Infographics

A representation with the words ideal gas law on the top. There is an equation that shows that the product of pressure and volume is equal to the number of particles multiplied by the Boltzmann’s constant and temperature. This is also written in words below with a note that the number of particles multiplied by the Boltzmann’s constant is equal to the number of moles multiplied by the gas constant.

Now, take a look at the pre-lecture reading and videos below.

Required Videos

ph202 Thermo equations of state(3min)

ph202 Thermo equations of state - ideal gas law(5min)

ph202 Thermo PV diagrams intro(1min)

Suggested Supplemental Videos

ph202 Thermo equations of state - non-ideal(2min)

ph202 Thermo equations of state - ideal gas law - empirically derived (9min)

ph202 Thermo ideal gas simple example(2min)


ph202 Thermo pressure thumb over hole example(3min)

OpenStax Section 13.3 | The Ideal Gas Law

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OpenStax Section 13.5 | Phase Changes

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OpenStax Section 13.6 | Humidity, Evaporation, and Boiling

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