Temperature, Thermal Expansion and the
Ideal Gas Law
Heating the air inside a hot air balloon raises the air’s temperature, causing it to expand, and forces air out the opening
at the bottom.The reduced amount of air means its density is lower than the outside air, so there is a net buoyant force upward on the balloon.
 We consider a particular system meaning a particular
environment
 The goal is to describe the state of the system from
either
–  A microscopic point of view where the description would
involve details of the motion of all the atoms and molecules
making up the system.
–  Or macroscopic point of view which involves a description in
tems of quantities that are detectable directly by our senses
or instruments, such as volume, pressure and temperature.
  The description in terms of macroscopic quantities is
called thermodynamics
–  and the quantities used to describe the system are called
State variables
For example the state of a gas in a contained can be described
using three variables, volume, pressure and temperature.
Atomic Theory of Matter
 Matter is made up out of atoms (atom = indivisible in
greek)
 We speak about relative mass of individual atoms
–  Atomic mass or molecular mass is based on arbitrarily assigning
the abundant carbon atom 12C the atomic mass of exactly 12.0000
unified atomic mass units (u)
Atomic arrangements in
a) a crystalline solid,
b) a liquid,
c) a gas
Example: Distance between atoms. The density of copper
is 8.9 x 103 kg/m3 and each copper atom has a mass of
63u. Estimate the average distance between the
centers of neighboring copper atoms
Solution: The mass of 1 copper atom is 63 u = 63x1.66
10-27 kg = 1.05x10-25 kg. This mean that in a cube of 1
m on a side (Volume 1 m3) there are:
The volume of a cube of side l is V= l3 therefore on the
edge of the 1-m long cube there are (8.5x1028 )1/3
atoms = 4.4x 109 atoms. Hence the distance for
neighboring atoms is
  Temperature is a measure of
how hot or cold something is.
  Most materials expand when
their temperature is increased
  The electrical resistance of
matter changes with
temperature
  Color radiated by objects
changes with temperature.
Solids as iron glow orange or
even white at high
temperatures
  Instruments designed to
measure temperature are called
thermometers
Thermometers built by the
Academia del Cimento (1657-1667)
EXPANSION JOINT ON A
BRIDGE
Temperature scales
In order to measure temperature a scale needs to be defined
The most common scale today is Celcius scale or Centigrade scale
In the U.S. the Fahrenheit scale is common To define the scale two
reproducible fixed points are defined:
Freezing point Boiling point Mercury- or
alcohol-in-glass
thermometer
Bimetallic strip
Constant-volume gas thermometer
Thermal Equilibrium and the Zeroth Law
of Thermodynamics
If two systems are in thermal equilibrium with
a third system, then they are in thermal
equilibrium with each other.
This postulate is called the zeroth law of
thermodynamics
  Temperature is a property of a system that determines
whether the system will be in thermal equilibrium with
other systems.
  When two systems are in equilibrium their temperatures,
are, by definition, equal and no net thermal energy will be
exchanged between them.
Thermal Expansion
 Linear expansion
Experiments indicate that the change in length
of
almost all solid is, to a good approximation, directly
proportional to the change in temperature
Is called the coefficient of thermal expansion
Does the whole gets smaller or larger if the ring is heated?
Volume Expansion:
is the coefficient of volume expansion
When
we can ignore the higher order terms Gas Tank in the Sun
  The 70-Liter (L) gas tank of a car is filled to the top with gasoline at
20ºC. The car sits in the sun and the tank reaches a temperature of
40ºC (104ºF). How much gasoline would you expect to overflow from the
tank?
  Both the gasoline and the tank expand as the temperature increases.
However the coefficient of expansion is different.
The gasoline expands to:
The tank expands to:
More than a liter of gasoline could spill out
Anomalous behavior of water below 4º C
a)  Volume of 1.00000 g of water near 4ºC as a function of temperature b)  Density vs. temperature
The Gas Laws and Absolute Temperature
  For a gas it is more meaningful to describe the relation between
volume, pressure, temperature and mass of the gas than just the
volume expansion.
  In this case we speak of writing down the equation of state (to
describe the physical condition of the system)
  Also if the state of a system is changed we wait to have the
same pressure and temperature throughout
–  We will consider only equilibrium states
–  And temperature far from liquefaction
  For a given quantity of gas it is found experimentally that the
volume of a gas is inversely proportional to the absolute
pressure applied to it when the temperature is kept constant Volume of a fixed amount of gas as a function
of Temperature
  The relation is known as
Boyle’s Law: Robert Boyle
(1627-1691)
  This law can also be written as
  The pressure here is not
gauge pressure but absolute
pressure
Charles Law (1746-1823):
The volume of a given amount of gas is
directly proportional to the absolute
temperature when the pressure is constant
Gay-Lussac Law (1778-1850):
At constant volume, the absolute pressure of a gas is directly proportional to
the absolute temperature Ideal Gas Law/Equation of state of an
ideal gas
  R is the universal gas constant
  Example the number of moles in 132 g
of CO2 (molecular mass 44 u) Examples
Standard temperature and pressure (STP) mean
C
 Volume of 1 mole at STP
–  Determine the volume of 1.00 mol of any gas, assuming it
behaves like an ideal gas, at STP.
 Use the ideal gas law to evaluate the volume
 Since 1 liter (l) is 1000 cm3 = 1.00 x 10-3 m3 , 1.00 mol
of ideal gas of STP has V = 22.4l
Helium Balloon
  A helium party balloon, assumed to be a perfect sphere, has a
radius of 18.0 cm. At room temperate (200C), its internal pressure
is 1.05 atm. Find the number of moles of helium in the balloon and
the mass of helium needed to inflate the balloon to these values
  We use the ideal gas law to find n
–  The pressure is given as 1.05 atm = 1.064 x 105 N/m2.
–  The temperature must be expressed in Kelvins T = 200C = (20 +
273 )K = 293 K
–  We use R = 8.314 J/(mol.K) because we are using the SI unit
system
–  The mass of helium ( of atomic mass 4.00 g/mol )can be
obtained from
Check tires cold
  An automobile tire is filled to a gauge pressure of 200 kPa at 100C.
After a drive of 100 km, the temperature within the tire rises to 400C.
What is the pressure within the tire now?
  We do not now the number of moles of gas , or the volume of the tire,
but we assume that they are constant. The we use the ratio form of
the ideal gas law. Since
–  Thus
–  Since the pressure given is gauge pressure we need to add the
atmospheric pressure to get the absolute pressure
–  We convert the temperature to Kelvins
  We subtract the atmospheric pressure to find the gauge pressure P2 = 232 kPa
Kinetic Theory of Gases
 The ideal gas law and the molecular
interpretation of Temperature
1.  There are a large number of molecules moving in
random directions with a variety of speeds.
2.  The molecules are on average far apart from one
another. Average separation much larger that the
size of the molecules
3.  Molecules are assumed to obey the law of
classical mechanics (potential energy small
compared to kinetic energy)
4.  Collisions with the wall are assumed to be
completely elastic
Temperature related to Average Kinetic energy of Molecules
Thermal Energy of a system