Class 35
Ch 13 Temperature and Kinetic Theory
Concepts for the rest of the course --- Temperature, Heat, Entropy,
Thermodynamics
The Atomic Theory of Matter
Greek name Democritus speculated that matter was made up of indivisible units called atoms.
Brownian Motion
http://www.aip.org/history/einstein/brownian.htm
http://www.youtube.com/watch?v=4tt7M2fpI6U
http://www.physics.emory.edu/~weeks/squishy/BrownianMotion.gif
Random Walk.
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Class 35
3 Main States of Matter
In liquids the motion of the particles is detectable in Brownian motion.
Temperature
Temperature is something which we have a strong intuitive feeling for, yet if we ask for a precise
definition of it we will have trouble. In fact temperature is the quantity in all of physics whose
definition is most difficult to put in a precise manner. A large part of this chapter is an effort to establish
the definition of temperature.
Is temperature a new basic quantity, such as mass, or is it related to mechanical states in some way?
Historically the first view held, until 19 th century.
The theory which relates temperature to the motion of particles is called “kinetic theory”
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Thermal Expansion
Temperature Scale
Put a thermometer in boiling water make a mark, then put it in water with ice in it and make a second
mark.
Then divide the interval between these marks into 100 units.
With this device we can measure temperature.
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Thermal Equilibrium
If I put a thermometer in a liquid, the thermometer will soon become the same temperature as the liquid
This condition, in which 2 objects come to the same temperature through direct contact is called
thermal equilibrium.
The Zeroth Law of Thermodynamics
If 2 systems are both in equilibrium with a third system, then the first 2 systems are in equilibrium
with each other.
Now that we have a definition of thermal equilibrium, we can make a provisional definition of
temperature,
Temperature is the property of a system which determines if the system will be in thermal equilibrium
with another system.
When systems are in thermal equilibrium, then their temperatures are equal.
Thermal Expansion
For solids, the change in length of the solid is linearly related to the change in temperature.
 L= L 0  T
 is the coefficient of linear expansion, and is different for every different material.
Anomalous thermal expansion of water.
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The Gas Laws and Absolute Temperature
Temperature is a characteristic of objects make up of a large number of atoms of molecules.
The simplest object make up of a large number of particles is a gas. Therefore, the elucidation of
temperature is most readily done through the behavior of gasses.
If I have a gas in a container it will have a certain pressure and a certain volume.
The pressure and the volume are related to the temperature by
PV ∝ T
This proportionality can be turned into an equation by use of the concept of moles
Mole
The precise definition of a mole is
A mole is the amount of a substance which contains as many atoms or molecules as there are in 12 gms
of Carbon 12.
A simpler definition of a mole can be had through the useful concept of molecular mass.
molecular mass
The molecular mass is the mass of an atom or molecule in atomic mass units
Atomic Mass Units
An atomic mass unit, u, is
1
of the mass of Carbon-12.
12
1 u =1.6605∗10−12 kg
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With this definition of molecular mass we can define a mole as
A mole is a number of grams of a substance numerically equal to the substance's molecular mass.
For example to CO2 , the molecular mass is 44 u. Therefore there would be 44 gms in one mole of CO 2
If one had 132 gms of CO2 , then one can compute the number mole by
n [ moles]=
132 g
=3.0 mole
gm
44
mole
If we have the amount of gas in moles we can write the ideal gas law as
PV =nRT
where n is the number of moles of the gas, and R is the universal gas constant
R=8.314
J
mole∗K
where K is degree of temperature on the Kelvin or absolute temperature scale.
The Universality of R for all gasses
The fact that all gasses obey the ideal gas law is an indicator of the simplicity of the gas state of matter.
The pressure and volume depend only on the amount of gas present and the temperature.
Avogadro's Number
Because of the definition of a mole the number of atoms or molecules in a mole, of any substance is the
same. That number is called Avogadro's Number
N A=6.02∗20 23
Kelvin or Absolute Temperature
To understand what absolute temperature is we need to look at the volume of a gas whose pressure is
kept constant while the temperature is changed.
We see that the graph is a straight line.
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If we extrapolate that straight line to a point where the volume of the gas becomes zero, the
extrapolation intercepts the x axis at 3T=−273 o C
We can then make a new temperature scale in which this point of intersection is called zero, and the
size of the temperature units is the same as the Celsius scale.
The freezing point of water on this scale will be 273 oK.
Calculations Using the Ideal Gas Law
Standard Conditions
Standard Conditions is a common set of temperature and pressure, corresponding to the freezing point
of water and 1 atmosphere of pressure.
Example 13-10
Determine the volume of 1 mole of ideal gas at standard conditions.
We use the idea gas law and solve to V
V=
nRT
P
J
∗273o K
o
mole K
=22.4 10−3 m3
5
2
1.01310 N / m
1.00 mole∗8.314
V=
A common measure of volume is a liter which is 1000 cm3.
We can convert the above answer into liters
22.4∗10−3
m3∗100cm3
=22.4∗1000cm 3=22.4 L
3
1m
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Example 13-12
Estimate the mass of air in a room whose dimensions are 5m x 3m x 2.5m , at STP
First we estimate the number of moles in the room, by calculating the volume of the room
n=5m ∗3m ∗2.5m
1 mole
≈1700mole
22.4∗10−3 m3
To calculate the mass we need to estimate the molecular mass of the average air molecule.
Air is composed of 20% oxygen, O2, and 80% nitrogen, N2.
The molecular mass of O2 is 2 * 16u = 32u, and the molecular mass of N2 is 2 * 14u = 28u
To find the average we use the relative percentage,
mav =.20∗32 u.80∗28u=28.8u
According to the definition of a mole, a mole of air has a mass of 28.8 gm = .028 kg
So the mass of the air in the room is
m≈1700 mole∗0.029
8
kg
≈50kg
mol
Class 35
The Kinetic Theory of Matter and the Molecular Interpretation of
Temperature
Note that, although the graph of the volume of a gas at constant pressure gives us a definition of
absolute temperature, we still have not related temperature to any of the fundamental mechanical aspect
of things such as mass, velocity, etc.
This connection if supplied by the Kinetic Theory of Matter, and the Molecular Interpretation of
Temperature.
Postulates of kinetic theory of an Ideal Gas
1. The gas is made up of a large number of molecules, N, each of identical mass, m, and each is
moving in random direction with a distribution of different speeds.
2. The molecules of the gas are far apart, I. e. there separation is far greater than the diameter of
the molecule.
3. The sole interaction between the molecules is collision and these collisions obey the laws of
classical mechanics.
4. The collisions between molecules are perfectly elastic.
It can be shown that the result of these hypotheses is that
1
3
2
KE av = m v av = k T
2
2
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