Thermodynamics

1
Thermodynamics

• Chapters 10 Thermal Physics

2
Temperature and Heat

• Temperature
• Relative measure of the hotness or the coldness
  of an object
• Temperature sense is
• Based on a human scale
• Somewhat unreliable
• Heat
• Net energy transferred between objects because of
  a temperature difference
• Energy in transit

3
Heat vs. Temperature

• Heat flow is measured with an instrument called a
  calorimeter.
• Heat is measured in Joules (J).
• Heat is NOT measured with a thermometer.
• Temperature is measured with a thermometer.
• Temperature is measured in degrees (oC or oF).

4
Vocabulary

• Thermal contact exists if 2 objects can
  exchange energy between them
• Thermal equilibrium objects in thermal contact
  with each other no longer exchange energy
• Consider this scenario

5
Scenario

• Consider 2 objects, A and B, which are not in
  contact with each other.
• A third object, C, acts as a thermometer.
• C is placed in thermal contact with A until
  thermal equilibrium is reached
• C is then placed in thermal contact with B until
  thermal equilibrium is reached
• If Cs thermometer reading is the same for A and
  B, then A and B are also in thermal equilibrium
  with each other.

6
Zeroth law of thermodynamics

• If 2 bodies are separately in thermal equilibrium
  with a third body, then the first 2 bodies will
  be in thermal equilibrium with each other if
  placed in thermal contact.

2 objects in thermal equilibrium with each other
are at the same temperature.
7
Thermometers and Temperature scales

• Thermometers are devices used to measure the
  temperature of a system
• Make use of a change in some physical property
  with temperature
• Usually change in volume (thermal expansion)
• Calibrated so that a numerical value can be
  assigned to a given temperature.
• Usually based on ice point and steam point of
  water

8
Thermometers

• If molecules are moving quickly they have
• Lots of Kinetic Energy
• Lots of Heat
• So the temperature is high
• If molecules are moving slowly they have
• Low Kinetic Energy
• Little Heat
• So the temperature is low

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Temperature Scales

• Celsius (Centigrade)
• Ice point 0o C
• Steam point 100o C
• 100 equal intervals between ice steam

• Fahrenheit
• Ice point 32o F
• Steam point 212oF
• 180 equal intervals between ice steam

A Celsius degree is 1.8 times larger than a
Fahrenheit degree.
10
Converting from one Temp scale to another

• From Fahrenheit to Celsius
• TC 5/9 (TF 32)
• From Celsius to Fahrenheit
• TF (9/5)TC 32
• TF 1.8TC 32
• At what temperature will the readings be the same
  number?
• -40oF -40oC

11
Human Body Temperature

• accepted value 98.6oF
• Actual normal human body temp ranges from 96oF
  to 101oF when taken orally
• Average is actually 98.2oF
• Women have a slightly higher average than men
• Body temp is typically lower in the morning
• After sleeping
• Digestive processes are at a low point
• Fever
• 102oF to 104oF
• At or above 106oF is extremely dangerous
• Enzymes for certain chemical reactions in the
  body begin to be inactive
• Total breakdown of body chemistry can result
• Decrease in body temp
• Memory lapse, slurred speech, erratic heartbeat,
  loss of consciousness
• Slows body chemical reactions and cells use less
  oxygen
• Sometimes beneficial
• Before some surgeries a patients body temp may
  be lowered to avoid damage to organs

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Absolute Temperature Scale

• Constant-volume gas thermometer
• When the column of mercury is adjusted so the top
  of the mercury is at the "0" mark on the scale,
  the volume of the gas is a constant.
• The height of the mercury column, h, then
  measures the pressure of the gas. This pressure
  can be used as a measure of temperature.
• The pressure of the gas is a thermometric
  property.

13
Absolute Temperature Scale

• Such a constant-volume gas thermometer gives
  easily reproducible results over a wide range of
  temperatures.
• It is accurate over a wide range of conditions
  -- as long as we avoid getting close to the
  condensation temperature of the gas.
• It is interesting to extrapolate this graph to
  see where the pressure would go to zero.

How its done in one lab
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Absolute Temperature Scale
Absolute zero

• If we use constant-volume gas thermometers filled
  with gasses of different kinds or at different
  pressures, we will still measure the same
  temperatures. That is why a constant-volume gas
  thermometer is useful!
• And an extrapolation of each of their graphs to
  zero pressure occurs at the same temperature, -
  273.15oC.

15
Absolute Temperature Scale

• We use this to create a new temperature scale,
  the absolute temperature scale.
• This common temperature at which all the
  constant-volume gas thermometers converge is
  called absolute zero.
• The size of the units on this scale are the same
  as on the Celsius temperature scale.
• The units are called kelvins and are indicated by
  K -- without a "degree" sign. This is also known
  as the Kelvin temperature scale.

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Kelvin

• The SI unit for temperature is the kelvin, but we
  hardly use it in any equations.
• As of 2003, researchers had gotten as low as
  0.5x10-9 of a degree above absolute zero
• If temp could reach 0 K
• the kinetic energy of the molecules would go to
  zero
• no motion
• molecules would settle at the bottom of the
  container.

Kelvin C 273
C Kelvin - 273
17
Thermal Expansion

• What happens to the length of a rod when you heat
  it?
• The length of the rod increases by ?L
• This phenomenon is known as thermal expansion.
• Thermal expansion joints must be included in
  buildings, roads, bridges, etc., to compensate
  for this type of expansion.

?L L - LO or L LO ?L
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Thermal Expansion

• Why?
• As temperature increases, atoms vibrate with
  greater amplitude, pushing atoms away from each
  other.
• This results in the entire solid expanding.
• For objects where one length is much greater than
  the other dimensions, we are most concerned about
  linear expansion.
• ?L is proportional to ?T and Lo
• a is called the average coefficient of linear
  expansion.

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Coefficients of linear expansion

• As with friction, thermal expansion is dependent
  on the material involved.
• P. 319 of your book has a similar table.
• Notice that the units are not in /kelvin, but /oC.

20
Example

• A copper pipe is 5m long at room temperature
  (68oF). If hot water is running through it, it
  heats up to 104oF. What is the change in length
  of the beam?

Looking for ?L
Given 5m 68 oF 104oF copper
(17 x 10-6)(5)(40-20) 0.0017m
Lo Ti 20oC Tf 40oC a 17 x 10-6 /oC
What happens if ?L is negative? Not expansion
Material got colder contraction
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How does a thermostat work?

• A coil of wire inside the thermostat is made of 2
  different types of metal (bimetallic strip) with
  different coefficients of thermal expansion .
• These differences cause the metal to expand or
  contract differently.
• When one shrinks, the other doesnt, causing the
  wire to bend one way or the other.
• If the wire bends too far, the switch turns on,
  telling the heater to start.
• How thermostats work Explain that Stuff!

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• This describes what happens when a rod is heated.
  For such a rod, we would only be interested in
  its length.
• What happens when a plate is heated? And what
  happens to a hole cut into a plate as the whole
  thing is heated? If you cut a hole out of a piece
  of dough and bake it -- as in a donut -- the
  dough will expand and make the hole smaller.
• That is not the case for heating a metal plate.
  The hole expands along with the rest of the plate.

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What about a three-dimensional volume? How does
heating affect that?
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So thermal expansion acts in all directions.
(length, width and height)
Linear expansion
Volume expansion
This works for area too. ? 2a
Gamma
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How weird is water?

• Like other liquids, water contracts as it gets
  colder -- until it reaches 4o C. Then it expands!
  
• As water gets colder, its density increases until
  it reaches 4oC. Then its density decreases.

As water gets colder, its density increases --
meaning it will drift to the bottom of, say, a
lake until it reaches 40 C. Then its density
decreases causing it to float to the top of, say,
a lake.

• If water behaved as other liquids, as the air
  temperature became colder,
• the surface water would become colder and would
  drift to the bottom.
• lakes would freeze from the bottom up they
  would freeze solid.
• Actually as the air temperature becomes colder,
• the surface water becomes colder and drifts to
  the bottom, until the surface water temperature
  reaches 4o C.
• Then additional cooling of the water makes that
  colder water more buoyant (or frozen) and it
  remains at the surface.
• Therefore, freezing occurs at the top of a lake
  and the water underneath remains liquid

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Macroscopic Description of an ideal gas

• In this section we want to know about the
  properties of a gas that
• Has a mass of m
• Is confined to a container of volume V
• At pressure P
• At temperature T
• The equation that relates all of these things is
  calledthe equation of state
• Generally, this equation is very complicated, but
  if the gas is maintained at a very low pressure
  (low density), the equation becomes quite simple.
• An ideal gas is a theoretical gas composed of a
  set of randomly-moving point particles that
  interact only through elastic collisions.
• All gases approach a unique ideal gas at low
  densities, most even at room temperature and
  atmospheric pressure.

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Ideal Gas Law
Write this down!

• PV nRT
• P pressure in atm (or Pa)
• V volume in liters (or m3)
• n moles
• R universal gas constant
• 0.08206 L atm/ molK
• 8.31 J/ molK (if units are in Pa and m3)
• T temperature in kelvins

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Amedeo Avogadro, conte di Quaregna e di Cerreto
(1776 - 1856)

• It is convenient to express the amount of gas in
  a given volume in terms of the number of moles
• 1 mole number of atoms in a 12g sample of
  carbon-12
• 6.02 x 1023 (Avogadros number)
• number of moles total mass /molar mass

Write this down!
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• In 1811, Avogadro hypothesized that equal
  volumes of gas at the same temperature and
  pressure contain the same number of molecules.
  AND One mole quantities of all gases at
  standard temperature and pressure contain the
  same number of molecules.

number of moles total number of molecules (N) /
Avogadros number
Write this down!
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Ideal Gas Law

• With this we can rewrite PV nRT RT
• or
• PV NkBT

Boltzmanns constant 1.38 x 10-23 J/K
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The Combined Gas Law
The combined gas law expresses the relationship
between pressure, volume and temperature of a
fixed amount of gas.
(n stays the same) From this relationship, if one
variable is held constant other laws have been
derived
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Boyles Law
Pressure is inversely proportional to volume when
temperature is held constant.
33
Charless Law

• The volume of a gas is directly proportional to
  temperature, and extrapolates to zero at zero
  Kelvin if P is constant.

Temperature MUST be in KELVINS!
34
Gay Lussacs Law
The pressure and temperature of a gas
are directly related, provided that the volume
remains constant.
Temperature MUST be in KELVINS!
35
Example

• A 10L tank is to be filled with oxygen at 20oC to
  a pressure of 50atm. Find the mass of oxygen
  required.

Looking for m.
V 10L
P 50atm
T 20oC 293K
R 0.08206 L atm/mol K
What if the gas were helium?
36
Example

• An automobile tire is inflated with air
  originally at 10.0oC to a gauge pressure of
  200kPa. After driving 100km, the temperature
  within the tire increased to 40.0oC. What is the
  tire pressure now?

221kPa
37
Kinetic Theory of Gases

• If the molecules of a gas are viewed as colliding
  objects, Newtonian Laws of Mechanics can be
  applied to each molecule of that gas.
• Because of the large number of particles, a
  statistical approach is necessary p. chem.
• Theoretical physics derived the ideal gas law
  from mechanical principles
• Causing a new interpretation of temperature in
  terms of the kinetic energy of these gas
  molecules.
• Pressure and temperature can be understood by
  knowing what happens at the atomic level.

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Kinetic Theory of Gases 5 Assumptions

1. The number of molecules in the gas is large and
   the average separation between them is large
   compared to their dimensions.
2. The molecules obey Newtons laws of motion, but
   as a whole they move randomly.

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Kinetic Theory of Gases Assumptions, cont.

1. The molecules interact only by short-range forces
   during elastic collisions
2. The molecules make elastic collisions with the
   walls
3. The gas under consideration is a pure substance,
   all the molecules are identical

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Pressure of an Ideal Gas

• Because of these assumptions, we can figure out
  an expression for the pressure of N molecules of
  an ideal gas in a container of volume V.
  Derivation is on p.329-330 of your text.

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Pressure, cont

• The pressure is proportional to the number of
  molecules per unit volume and to the average
  translational kinetic energy of the molecule
• Pressure can be increased by
• Increasing the number of molecules per unit
  volume in the container
• Increasing the average translational kinetic
  energy of the molecules
• Increasing the temperature of the gas

42
Molecular Interpretation of Temperature

• Temperature is proportional to the average
  kinetic energy of the molecules
• The total kinetic energy is proportional to the
  absolute temperature

43
Internal Energy

• In a monatomic gas, the KE is the only type of
  energy the molecules can have
• U is the internal energy of the gas
• In a polyatomic gas, additional possibilities for
  contributions to the internal energy are
  rotational and vibrational energy in the molecules

44
Speed of the Molecules

• Expressed as the root-mean-square (rms) speed
• At a given temperature, lighter molecules move
  faster, on average, than heavier ones
• Lighter molecules can more easily reach escape
  speed from the earth

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Some rms Speeds
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Example

• What is the average (rms) speed of a helium atom
  in a helium balloon at room temperature? (Mass of
  a helium atom is 6.65x10-27kg)

Given m 6.65x10-27kg T 20oC 293K kB
1.38x10-23J/K
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Maxwell Distribution

• A system of gas at a given temperature will
  exhibit a variety of speeds
• Three speeds are of interest
• Most probable (mp)
• Average
• rms

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Maxwell Distribution, cont

• For every gas, vmp lt vav lt vrms
• As the temperature rises, these three speeds
  shift to the right
• The total area under the curve on the graph
  equals the total number of molecules

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Diffusion

• When you can smell something from a source far
  away from your nose implies that molecules can
  get from one place to another in the air.
• Random molecular mixing, where molecules move
  from higher concentration to an area of lower
  concentration
• The rate of diffusion depends on the rms speed of
  its molecules.
• Even though gases seem to have large average
  speeds, molecules do not fly from one place to
  another, but there are frequent collisions
  drift

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• Effusion gases diffusing through porous or
  permeable materials even slower than diffusion.