absolute zero

The coldest possible temperature at which the average energy per degree of freedom is zero. Turns out this is actually impossible due to quantum mechanical effects, a fact stated as the Third Law of Thermodynamics.

analytical methods

Analyzing a situation primarily by using pencil-and-paper in contrast to using a computer model to understand the physics of the situation.

Boltzmann constant

a physical constant that connects the microscopic and macroscopic regimes; k = 1.38 x 10^(-23) J/K.

closed system

A collection of objects where energy cannot enter or leave. It can be exchanged among the objects within the system, but cannot leave, nor can more energy come in.

computational methods

Giving the fundamental principles of physics to a computer and using it to model in simulation the behavior of a system.


geometric shapes which are identical except for perhaps being rotated or flipped.

coordinate system

A way of quantifying space: you define zero and the direction which you will consider to be positive.


A place I can put energy. The molecules of an ideal gas, for example, have three degrees of freedom corresponding to motion in each of the three dimensions: front/back, left/right, and up/down.

dependent variable

the variable that is being measured; usually plotted along the[latex]\boldsymbol{y}\text{-axis}[/latex]


One of the three different independent directions in which you can move: left/right (generally referred to a x), up/down (generally referred to as y), and front/back (generally referred to as z). In some contexts, time can also be considered a dimension, but this consideration is beyond the scope of this course.


A possible direction of motion. Our world generally has three spatial dimensions: up/down, left/right, and front/back though lower dimensional systems can exist by constraining motion in specific directions only.


The capacity of an object to do work. This capacity does not have to be realized, it just has to exist.


A measurement of the total number of microstates for a given macrostate.


A push or a pull on an object. Forces have both a size (magnitude) and a direction.

Fundamental Postulate of Statistical Mechanics

All microstates in a given macrostate are equally likely.


The diffusion of energy from a region of high concentration to a region of low concentration.

ideal gas

An idealized model of a gas. In this model, the molecules of the gas are visualized as spheres with mass, but zero size. Having zero size implies that these molecules cannot collide with one another, but only with the walls of their container. Thus, the molecules travel in straight lines until they hit the wall from which they bounce without a loss of energy.

independent variable

the variable that the dependent variable is measured with respect to; usually plotted along the[latex]\boldsymbol{x}\text{-axis}[/latex]

Kelvin temperature scale

A temperature scale which starts at absolute zero and has steps the same as a degree Celsius.

kinetic energy

The capacity to do work (push or pull on something for a distance) arising from an object's motion. We can either think of the bulk motion of an object or the net energy from the random motions of the constituent particles due to their temperature.


A "overall" picture of a system. This can be defined however the observer wishes. It could include such overall properties as volume, temperature, density, total energy, or more "contrived" properties such as the number of 1's that result from rolling a handful of dice.


The amount of "stuff" in an object. This is independent of the planet near which the object is located and is measured in kg.


The specific condition of each individual element of the system. If these are individual atoms, then we might speak of their positions, velocities, or other properties. In the case of multiple dice, we might speak of the result of each individual dice thrown.

open system

A collection of objects which is free to exchange energy with its environment.


The location in a coordinate system from which all distances are measured.

potential energy

The capacity to do work due to the relative positions of different objects within a system. There are many different kinds. The ones we will focus on here are gravitational, spring, and chemical.


How much a force is spread out over an area.


the fraction of time a given outcome occurs if the process is repeated an infinite number of times


A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the simulation.

“Simulation.” Wikipedia, 28 Aug. 2022. Wikipedia,


The "rise over run" of a graph often written as Δy/Δx


The average kinetic energy per degree of freedom within an object/system.

thermal energy

The total energy present in a system associated with the average kinetic energy of the different molecules.

Third Law of Thermodynamics

Absolute zero is impossible.


A quantity with magnitude and direction.


A quantity with magnitude and direction.


The force with which a planet pulls on an object. Depends on the mass of the object and the strength of the planet's gravity.


A force applied for some distance: when I push or pull on an object for some distance, I am doing work on it.


the[latex]\boldsymbol{y}\text{-value}[/latex]when[latex]\boldsymbol{x}=\:0,[/latex] or when the graph crosses the[latex]\boldsymbol{y}\text{-axis}[/latex]


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