.. _lecture1:

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:  :download:`pdf <_pdfs/slides/lecture1.pdf>`
   
   
Screencast
~~~~~~~~~~


.. raw:: html

   <iframe width="560" height="315" src="https://www.youtube.com/embed/c1R9PHHrS_0" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>


   <iframe width="560" height="315" src="https://www.youtube.com/embed/BXHTrU7RMHA" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>

   
   <iframe width="560" height="315" src="https://www.youtube.com/embed/7DMICyuM1tg" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>

.. raw:: latex

 This lecture is available as a YouTube recording at these links:  \href{https://www.youtube.com/embed/c1R9PHHrS_0}{lecture1}., \href{https://www.youtube.com/embed/BXHTrU7RMHA}{lecture2},  \href{https://www.youtube.com/embed/7DMICyuM1tg}{lecture3}.
 

Key Definitions
---------------
 
.. note::  


   :index:`Mole`:
      a mole is a collection of :math:`N_A=6.02 \times 10^{23}` particles where :math:`N_A` is known as the Avogadro number.

   :index:`Thermodynamic limit`:
      is the regime where properties of many particles can be described by ensemble averages.

   :index:`Ideal gas`:
      an ideal gas is a gas where the individual particles do not interact with each other.

   :index:`Intensive variable`:
      an intensitve variable is a thermodynamic variable that does not depend on the size of the system considered.

   :index:`Extensive variable`:
      An extensive variable is a thermodynamic variable is a variable that depends on the size of the system considered.

   :index:`Stirling approximation`
      Stirling approximation is an approximation for the logarithm of a factorial (it is very accurate when :math:`n` is large):

      .. math::
	
	 \ln n ! \approx n \ln n-n

   :index:`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.

   :index:`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 :ref:`genindex`.
   
Test your knowledge
-------------------

1. Among the examples listed below, which one is not an example of a
   system at the thermodynamic limit?

   A. Distribution of rain over a large area for a long time?
   B. water droplets falling from a leak in the roof?
   C. Clouds in the sky?
   D. The temperature of a large number of particles (:math:`N_A`). 

2. What is an extensive variable?

   A. a variable whose magnitude depends on the system size
   B. a variable whose magnitude does no depend on the system size
   C. It depends on the context.

3. Speaking of thermodynamic limit:

   A. it is a situation where temperature tends to zero
   B. it is a situation where fluctuations in a quantity are much
      smaller than the average value of that quantity
   C. It depends on the context.

4. When can we describe a system as an ideal gas when

   A. The particles do not interact attractively
   B. The particles do not interact repulsively
   C. The particles do not interact at all 
   D. It depends

5. What is heat?

   A. A form of energy stored in a closed system 
   B. A form of energy that is transferred from a hot body into a cold body
   C. A synonym of temperature
   D. None of the above

6. Is heat capacity at constant pressure larger than heat capacity at constant volume?

   A. Yes
   B. No
   C. It depends

7. How many ways can you pick 5 objects from a collection of 9?

   A. 126
   B. 128
   C. 63
   D. 54

8.  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?

    A.  After :math:`n` steps, the drunken salesman will, on average,
        end up at a distance :math:`d = n`.
    B.  After :math:`n` steps, the drunken salesman may have
	beenfound, at some point, at a distance of about :math:`\sqrt{n}`
	away from his starting point, for a large enough value of
	:math:`n` .
    C.  After :math:`n` steps, the pedometer on the wrist of the
       drunken salesman will measure exactly :math:`n/2` steps by the
       time he reaches the end of the street.
    D.  None of the other answers is correct.

9. What is a Bernoulli trial?

   A. It is an event when Bernoulli went to jail because he stole a plane. 
   B. It is an experiment with only two possible outcomes
   C. It is the event when the definition of temperature was finalized



.. hint::
   
   Find the answer keys on this page: :ref:`answerkeys`. Don't cheat! Try solving the problems on your own first!

Homework Assignment
-------------------