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Lecture PHYSICS 22
Temperature and Ideal Gas
and Ideal Gas
Textbook Sections 14.1 14.3
Lecture 22
Purdue University, Physics 220
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Overview
Last Lecture
Speed of sound v = sqrt(B/)
Intensity level = (10 dB) log10 ( I / I0)
Standing Waves
fn = n v/(2L)
fn = n v/(4L)
open at both ends n=1,2,3,
open at one end n=1,3,5,
Doppler Effect fo = fs (v-vo) / (v-vs)
Beats = 1 ( )
2
L
1
2
Today
Temperature
Ideal Gas
Lecture 22
Purdue University, Physics 220
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Quiz
1) The intensity of a sound wave is directly proportional to
A) the frequency
B) the square of the speed of sound
C) the amplitude
D) the square of the amplitude
the square of the amplitude
2) If the distance to a point source of sound is doubled, by
If the distance to point source of sound is doubled by
what factor does the intensity decrease?
A) 1x
1x
B) 4x
C) 8x
D) 2x
Lecture 22
Purdue University, Physics 220
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Thermodynamics
Thermodynamics is about the transfer of energy between
systems of particles
systems of particles
Thermodynamics focuses on energy rather than forces
Conservation of energy is a key pillar of thermodynamics
of energy is key pillar of thermodynamics
It is also about the way changes in the energy of a system
affects its properties
affects its properties
Several new quantities, such as temperature and heat, are
needed to describe the properties of systems and their
interactions
Lecture 22
Purdue University, Physics 220
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System
A thermodynamic system
contains multiple particles,
usually a very large number
The particles in a system
particles in
are able to exchange
energy with one another
energy with one another
via collisions
Systems are able to
exchange energy with
other systems
The balloon filled with oxygen
molecules is an example of a
system
Lecture 22
Purdue University, Physics 220
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Properties of a System
Because of the extremely large numbers of molecules, it is
not feasible (although it is possible) to describe the system in
terms of Newtons Laws
In comparing two systems, they may not be identical on the
molecular level
The positions and velocities of all the molecules wont be the same
Various properties of the systems as a whole will be the
properties of the systems as whole will be the
same
System wide properties include temperature and pressure
We are generally interested in the macroscopic properties of
the system
They describe the behavior of the system on a scale much larger than
the individual particles
Macroscopic properties contrast with microscopic properties such as
properties contrast with microscopic
such as
position and velocity
Lecture 22
Purdue University, Physics 220
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Molecular Picture of Gas
Gas is made up of many individual molecules
is made up of many individual molecules
Number density is number of molecules/volume
N/V = /m
N/V
is the mass density
m is the mass for one molecule
is the mass for one molecule
Number of moles n = N / NA
of moles
NA = Avogadros number = 6.0221023 mole-1
NA= number of molecules per mole
number of molecules per mole
1 mole = amount of substance that contains as many
elementary entities as there are atoms in exactly 12
grams of carbon-12
Lecture 22
Purdue University, Physics 220
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Atoms, Molecules and Moles
1 mole = 6.022 1023 molecules (NA = Avogadros Number)
NA = Number of atoms or molecules that make a mass equal
to the substance's atomic or molecular weight in grams.
1 u = 1 atomic mass unit = (mass of 12C atom)/12
atomic mass unit (mass of 12 atom)/12
Approximately # of neutrons + # of protons
Atomic weight A
weight
1 u = 1.66 10-27 kg = 1gram/NA
Mass of 1 mole of stuff in grams = molecular mass in u
E.g. 1 mole of N2 has mass of 2 14 = 28 grams
Lecture 22
Purdue University, Physics 220
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Question
Which contains more atoms ?
B)
B) A mole of water (H2O)
(H
C) A mole of oxygen gas (O2)
A) Same
H2O (3 atoms)
O2 (2 atoms)
Lecture 22
Purdue University, Physics 220
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Question
Which weighs more ?
A)
A) A mole of water (H2O)
(H
B) A mole of oxygen gas (O2)
C) Same
H2O (M = 16 + 1 + 1)
O2 (M = 16 + 16)
Lecture 22
Purdue University, Physics 220
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Number Density ILQ
Two gas cylinders are filled such that they have the same
mass of gas (in the same volume) One cylinder is filled with
mass of gas (in the same volume). One cylinder is filled with
Helium, the other with Oxygen. Which container has the
larger number density?
A) Helium
B) Oxygen
C) Same
Helium molecule is lighter than Oxygen molecule. If you have
the same mass, you must have many more Helium molecules than
Oxygen. So the Helium number density is larger.
Lecture 22
Purdue University, Physics 220
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Internal Energy and Temperature
All objects have internal energy (measured in Joules)
random motion of molecules
kinetic energy
collisions of molecules gives rise to pressure
of molecules gives rise to pressure
Amount of internal energy depends on
temperature
related to average kinetic energy per molecule
how many molecules
mass
specific heat
related to how many different ways a molecule can move
translation
rotation
vibration
the more ways it can move, the higher the specific heat
Lecture 22
Purdue University, Physics 220
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Temperature
Temperature is not
contained in or
derivable from
Newtons laws
Temperature is a new
quantity and requires
a new unit of measure
A macroscopic
definition can be
definition can be
determined from
looking at two systems
looking at two systems
Lecture 22
Purdue University, Physics 220
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Temperature, cont.
Assume each system has its own temperature and
T1 > T2
System 1 is hotter than system 2
If the systems are brought into contact, energy is
the systems are brought into contact energy is
transferred spontaneously from system 1 to
system
system 2
Eventually, the two systems will have the same
energy
energy
They will reach thermal equilibrium
Their final temperature will be somewhere between
final temperature will be somewhere between
the two initial temperatures
Lecture University, 22
Purdue Physics 220
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Zeroth Law of Thermodynamics
If two (or more) objects are
two (or more) objects are
in thermal equilibrium, they
are at the same
are at the same
temperature.
If two objects are in
th
thermal equilibrium with a
third, then the two are in
equilibrium with each
ilib
other.
Lecture 22
Purdue University, Physics 220
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Temperature Microscopic View
If the temperature of the gas
increases, the average
speed of the gas atoms
increases and the pressure
increases, and the pressure
will also increase
A measurement of the
measurement of the
pressure gives a direct way
to find the temperature
Such a device is called a gas
thermometer
The temperature of a system
of particles is related to the
average particle speed
ti
Lecture 22
Purdue University, Physics 220
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Temperature Scales
Anders Celsius
(1701 - 1744)
Daniel G. Fahrenheit
(1686 - 1736)
Lord Kelvin
(1824 - 1907)
Lecture 22
Purdue University, Physics 220
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Temperature Scales
Celcius
Farenheit
Kelvin
212
100
373.15
32
0
273.15
9
F = C + 32
5
K = C + 273
Water boils
Water freezes
5
C = (F - 32)
9
C = K - 273
NOTE: K=0 is absolute zero, meaning (almost) zero KE/molecule
KE/
Lecture 22
Purdue University, Physics 220
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Temperature Scales, cont.
Two reference points are the temperatures at which water
freezes and boils
Celsius
Water freezes at 0 C
Water boils at 100 C
boils at 100
Fahrenheit
Water freezes at 32 F
Water boils at 212 F
Kelvin
Water freezes at 273.15 K
freezes at 273
Water boils at 373.15 K
No degree symbol is used with kelvins
All three scales are linear
The freezing and boiling points of water can be used to
develop conversions among the scales
Lecture 22
Purdue University, Physics 220
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Temperature Limits
Temperatures extend well above the boiling point of
water
water
They also extend below the freezing point of water
The lower limit to temperature is absolute zero
0K
Lecture 22
Purdue University, Physics 220
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Temp Scales ILQ
Two cups of coffee are heated to 100 degrees
Fahrenheit. Cup 1 is then heated an additional 20
th
20
degrees Centigrade, cup 2 is heated an additional
20 Kelvin Which cup of coffee is hotter?
20 Kelvin. Which cup of coffee is hotter?
A) One
One
B) Two
Two
C) Same
Same
K = C + 273
Lecture 22
Purdue University, Physics 220
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Sick ILQ
You measure your body temperature with a thermometer
calibrated in Kelvin. What do you hope the reading is
(assuming you are not trying to fake some sort of illness) ?
A) 307 K
B) 310 K
C) 313 K
F = 98.6
D) 317 K
5
C=
(F-32) = 37
9
K = C + 273 = 310
Lecture 22
Purdue University, Physics 220
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Charless Law
In 0C
In K
Inventor of the
hydrogen balloon
Lecture 22
If const P: V T
const P:
Purdue University, Physics 220
VT
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Other Empirical Laws
Gay-Lussacs Law
If const V: P T
Boyles Law
If const T: P 1/V
Avogadros Law
If const P and T: V N
Lecture 22
Purdue University, Physics 220
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The Ideal Gas Law
P V = N kB T
P = pressure in N/m2 (or Pascals)
V = volume in m3
volume in
N = number of molecules
T = absolute temperature in K
k B = Boltzmanns constant = 1.38 x 10-23 J/K
Note: P V has units of N-m or J (energy!)
Lecture 22
Purdue University, Physics 220
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The Ideal Gas Law
PV = NkBT
Alternate way to write this
N = number of moles (n) x NA molecules/mole
PV= NkBT
nNAkB T
n(NAkB)T
nRT
PV=nRT
n = number of moles
R = ideal gas constant = NAkB = 8.31 J/mol/K
Lecture 22
Purdue University, Physics 220
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Exercise
You inflate the tires of your car so the pressure is 30 psi,
when the air inside the tires is at 20 degrees C. After driving
on the highway for while the air inside the tires heats up to
on the highway for a while, the air inside the tires heats up to
38 C. Which number is closest to the new air pressure?
A) 16 psi
B) 32 psi
C) 57 psi
Careful, you need to use the temperature in K
P = P0 (38+273)/(20+273)
Lecture 22
Purdue University, Physics 220
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Question
What happens to the pressure of the air
happens to the pressure of the air
inside a hot-air balloon when the air is
heated? (Assume is constant)
heated? (Assume V is constant)
A) Increases
B) Same
B)
C) Decreases
C)
Balloon
Balloon is still open to atmospheric pressure,
so it stays at 1 atm
Lecture 22
Purdue University, Physics 220
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Question
What happens to the buoyant force on the
happens to the buoyant force on the
balloon when the air is heated? (Assume V
remains constant)
remains constant)
A) Increases
B) Same
B)
C) Decreases
C)
FB = V g
is density of outside air!
Lecture 22
Purdue University, Physics 220
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Question
What happens to the number of air molecules
happens to the number of air molecules
inside the balloon when the air is heated?
(Assume remains constant)
(Assume V remains constant)
A) Increases
B) Same
B)
C) Decreases
C)
PV = NkBT
P and V are constant. If T increases N decreases.
Lecture 22
Purdue University, Physics 220
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Balloon
In terms of the ideal gas law, explain briefly how a hot air
balloon works.
Once the air in a balloon gets hot enough, the net weight of the balloon
plus this hot air is less than the weight of an equivalent volume of
cold air, and the balloon starts to rise.
When temperature increases the volume of the gas increases, thus reducing the
density of the gas making it lighter that then surrounding air, which causes
the balloon to rise.
Note! this is not a pressure effect, it is a density effect. As T increases,
it
the density decreases the balloon then floats due to Archimedes principle.
The pressure remains constant!
Lecture 22
Purdue University, Physics 220
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Summary of Concepts
Temperature measure of average Kinetic Energy of
molecules
molecules
Gas made up of molecules
Ideal Gas Law PV = n R T
P = pressure in N/m2 (or Pascals)
pressure in N/m
Pascals)
V = volume in m3
n = # moles
moles
R = 8.31 J/ (K mole)
T = Temperature (K)
Temperature (K)
Lecture 22
Purdue University, Physics 220
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