Lecture 1: General Introduction

Note

Smooth seas do not make skillful sailors. — African Proverb

Warning

This lecture corresponds to Chapters 1, 2, and 3 of the textbook.

Summary

Attention

In this lecture, we introduce basic concepts such as thermodynamic limit, combinatorics, etc. The objective is to set the stage for this course and explain how understanding thermodynamics using statistical mechanics is a fascinating activity.

We stress that in order to make sense of thermodynamics requires a rigorous understanding of concepts but also the knowledge of a number of key definitions, as the precise meaning of a word ends up critical in our journey in thermodynamics and statistical mechanics.

The website will be organized as follows: after a summary, links to the slides and to the lectures will be provided. There will then be a section with all the key definitions found in the lecture, followed by a number of exercises.

Learning Material

Copy of Slides

The slides for Lecture 1 are available in pdf format here: pdf

Screencast

Key Definitions

Note

Mole:: a mole is a collection of $N_A=6.02 \times 10^{23}$ particles where $N_A$ is known as the Avogadro number.
Thermodynamic limit:: is the regime where properties of many particles can be described by ensemble averages.
Ideal gas:: an ideal gas is a gas where the individual particles do not interact with each other.
Intensive variable:: an intensitve variable is a thermodynamic variable that does not depend on the size of the system considered.
Extensive variable:: An extensive variable is a thermodynamic variable is a variable that depends on the size of the system considered.
Stirling approximation: Stirling approximation is an approximation for the logarithm of a factorial (it is very accurate when $n$ is large):

$\ln n ! \approx n \ln n-n$
Heat:: Heat is a form of energy in transfer. The definition means that a claim such as “the heat stored in the system” is non-sensical as the stress should be placed on transfer. We will study this in much more details throughout this course.
Heat capacity:: Heat capacity is the amount of energy needed to raise a system by one degree (Kelvin). It is also the energy released when the temperature is decreased by one degree.

A full list of terms, including the ones provided here, can be found in the Index.

Test your knowledge

Among the examples listed below, which one is not an example of a system at the thermodynamic limit?
1. Distribution of rain over a large area for a long time?
2. water droplets falling from a leak in the roof?
3. Clouds in the sky?
4. The temperature of a large number of particles ( $N_A$ ).
What is an extensive variable?
1. a variable whose magnitude depends on the system size
2. a variable whose magnitude does no depend on the system size
3. It depends on the context.
Speaking of thermodynamic limit:
1. it is a situation where temperature tends to zero
2. it is a situation where fluctuations in a quantity are much smaller than the average value of that quantity
3. It depends on the context.
When can we describe a system as an ideal gas when
1. The particles do not interact attractively
2. The particles do not interact repulsively
3. The particles do not interact at all
4. It depends
What is heat?
1. A form of energy stored in a closed system
2. A form of energy that is transferred from a hot body into a cold body
3. A synonym of temperature
4. None of the above
Is heat capacity at constant pressure larger than heat capacity at constant volume?
1. Yes
2. No
3. It depends
How many ways can you pick 5 objects from a collection of 9?
1. 126
2. 128
3. 63
4. 54
Imagine a random walk in one dimension (problem often called the drunken salesman). We will suppose that each step size to be equal to 1). What is the most accurate statement below?
1. After $n$ steps, the drunken salesman will, on average, end up at a distance $d = n$ .
2. After $n$ steps, the drunken salesman may have beenfound, at some point, at a distance of about $\sqrt{n}$ away from his starting point, for a large enough value of $n$ .
3. After $n$ steps, the pedometer on the wrist of the
drunken salesman will measure exactly $n/2$ steps by the time he reaches the end of the street.
1. None of the other answers is correct.
What is a Bernoulli trial?
1. It is an event when Bernoulli went to jail because he stole a plane.
2. It is an experiment with only two possible outcomes
3. It is the event when the definition of temperature was finalized

Hint

Find the answer keys on this page: Answers to selected test your knowledge questions. Don’t cheat! Try solving the problems on your own first!