Download Thermodynamics: Kinetic Theory

Thermodynamics:
Kinetic Theory
From Warmup
 The chapter just seemed like a ton of equations. I was
confused about what its point was. Can you explain that?
 Writing out 8-2A helped, but I still barely understand
anything after 21-2. The amount of equations that are
being juggled around and the various equalities and
substitutions being made are more than I can follow without
a clearer way to walk through it all.
 This chapter had, like, 44 equations. Do we have to know
them all?
 You are physicists. You should have a working knowledge of the
entire universe and everything it contains….
 I usually go over the whole derivation in class (“reading math”
is an important skill), but today we are pressed for time. So let
me give you the highlights….
 My slides (with more details than we will cover) are on the
course website.
Organization of Scientific
Theories
 Fields of science are organized hierarchically
 Simple theories of complex processes help us
understand the world.
 These simple theories operate as though the complexity
did not exist!
 Newtonian Mechanics vs. Quantum Mechanics
 Quantum Mechanics vs. string theory
 Thermodynamics vs. Statistical Mechanics
 Do you really need to know how all the molecules in a
gas are moving to understand how the gas will behave?
 But isn’t the behavior of the gas determined by the
motion of the molecules?
Emergence and complexity
Fluids
Solids
Chemistry
Biology
Macroscopic
Emergence
Complexity
Atoms
Microscopic
First principles
Microscopic Model to Macroscopic theory
d
Microscopic Model to Macroscopic theory
d
Microscopic Model to Macroscopic theory
(One particle)
(Whole gas)
d
On long time scales, the many small impulses
behave like a large, continuous force
Microscopic Model to Macroscopic theory
Microscopic Model to Macroscopic theory
Microscopic Model to Macroscopic theory
Success!
A microscopic model relating
to a macroscopic observable!
The Big Idea:
 If the molecular motion determines the behavior of the
gas, why do I not need to know all the microscopic
details to understand the gas?
 Only the average energy matters. I can distribute that
energy in different ways and the gas will look identical
to me on the macroscopic scale.
 Preview: Entropy (next section), Physics 360
Velocity, energy, and mass of
gases
In air, the molecular mass of oxygen molecules is 32 g/mol.
The molecular mass of nitrogen molecules is 28 g/mol.
Which molecules are traveling faster on average?
A) Oxygen
B) Nitrogen
C) Same Speed
Emergence
 Temperature and Pressure don’t “look” like energy and
collisions at first.
 They obey different laws
 Where is momentum conservation in PV = NkT?
 On large, macroscopic scales, new physics emerges, that is
fundamentally different from the microscopic physics.
 Macroscopic physical laws appear to exist almost independently
of the microscopic laws.
 Thermodynamics / Statistical Mechanics
 Knowing the microscopic laws does not mean you understand
the macroscopic laws.
 Understanding the relationship between the
microscopic/macroscopic is one of the major open problems in
fundamental science today.
Microscopic/Macroscopic Theories
Many theories have a macroscoipc/microscopic relationship:
 Thermodynamics / Statistical Mechanics
 Newtonian Mechanics / Quantum Mechanics
 Particle Physics / String Theory
 Climate / Weather
 Macroeconomics / Microeconomics
 Biology / Chemistry
 Material Science / Quantum Mechanics
Molar specific heat:
 If I add some energy to a gas, how much does its
temperature change? (Let’s assume there is no work,
i.e. Volume = constant)
 This equation is true for molecules with no internal
structure. If molecules can vibrate or rotate, they can
store more energy.
Equipartition Theorem:
 Each degree of freedom makes an equal contribution the
molar specific heat.

 In reality the situation is a bit more complicated….
 Quantum mechanics
 Gases can also do work
Hints of Quantum Physics
Clicker Quiz
What is the molar specific heat of an ideal gas of diatomic
molecules at room temperature?
A) 3/2 R
B) 4/2 R
C) 5/2 R
D) 6/2 R
E) 7/2 R
Count the degrees of freedom:
Translational motion: 3
Rotational motion: 2 (why not 3?)
Vibrational motion: 0 (why 0?)
Molar Specific Heats of a Gas
 Constant Volume – no work done
 Constant Pressure – work done on/by the gas
 Why are these different?
 Which is larger?