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 Understand the concepts of thermal equilibrium, heat transfer and the
Zeroth Law of Thermodynamics.
 Recognize the contributions of Galileo, Celsius, Fahrenheit, Joule,
Kelvin, and Ferdinand II to thermometry.
 Explain the major temperature scales and their relation to each other as
well solve temperature conversion problems.

3

 Understand the mechanics of thermal expansion.
 State Charles’ Law, Boyle’s Law, GayLussac’s Law, and the Ideal Gas
Law; solve problems dealing with each law.
 State and explain the assumptions of the Kinetic Theory of Gases.
 Describe the relationship between temperature and the average kinetic
energy of molecules.

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 Concerned with the concepts of energy transfers between a system and its
environment and the resulting temperature variations
 Historically, the development of thermodynamics paralleled the
development of atomic theory
 Concerns itself with the physical and chemical transformations of matter
in all of its forms: solid, liquid, and gas

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 Temperature is a measure of an object’s kinetic energy; temperature
measures how hot or how cold an object is with respect to a standard.
 A higher temperature object which is in contact with a lower
temperature object will transfer heat to the lower temperature object.
The objects will approach the same temperature, and in the absence of
loss to other objects, they will then maintain a constant temperature.
They are then said to be in thermal equilibrium.

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 The process by which energy is exchanged between objects because of
temperature differences is called heat
 Objects are in thermal contact if energy can be exchanged between them
 Thermal equilibrium exists when two objects in thermal contact with each
other cease to exchange energy

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 If objects A and B are in thermal equilibrium with a third object, C,
then A and B are in thermal contact with each other.
 Allows a definition of temperature

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 Two objects in thermal equilibrium with each other are at the same
temperature
 Temperature is the property that determines whether or not an object is
in thermal equilibrium with other objects

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 Thermometers are devices used to measure the temperature of an object or
a system
 Mercury thermometer is an example of a common thermometer

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 Make use of physical properties that change with temperature
 Many physical properties can be used
 volume of a liquid
 length of a solid
 pressure of a gas held at constant volume
 volume of a gas held at constant pressure
 electric resistance of a conductor
 color of a very hot object

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 At right is a Galileo Thermometer based on the early thermoscope that
Galileo invented in the 1600s. It works on the idea that as the air
temperature changes, so does the temperature of the water surrounding
the glass bubbles. This causes a change in the density of the water,
causing the glass spheres to move to different levels.

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 The first liquid filled thermometer was invented in about 1650 by
Ferninand II, the Grand Duke of Tuscany, one of Galileo’s buddies.
 Daniel Fahrenheit, a German
physicist working in Holland, invented the mercury thermometer in
1714. This invention was a more
accurate temperature gauge than the alcoholfilled thermometer which was
popular at the time.

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 Some thermometers give digital readouts based on electronic sensors.
 Some thermometers use mercury or
alcohol as the expansion agent. Some states are banning mercury filled
thermometers.

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 Thermometers can be calibrated by placing them in thermal contact with
an environment that remains at constant temperature
 Environment could be mixture of ice and water in thermal equilibrium
 Also commonly used is water and steam in thermal equilibrium

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 The most common scale is the Celsius, though in the United States the
Fahrenheit scale is common. Both of these scales use the freezing point
and boiling point of water at atmospheric pressure as fixed points. On
the Celsius scale, the freezing point of water corresponds to 0°C and
the boiling point of water corresponds to 100°C.
 On the Fahrenheit scale, the freezing point of water is defined to be
32°F and the boiling point 212°F. It is easy to convert between these
two scales by remembering that 0°C = 32°F and that 5°C = 9°F. The
Kelvin scale is based upon absolute zero
(273.15 °C), or 0 K.

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 Fahrenheit to Celsius: Tc = (5/9) (Tf32)
 For example, to convert a Fahrenheit temperature of 98.6 degrees into
degrees Celsius first subtract 32 from the Fahrenheit temperature to get
66.6. Then you multiply 66.6 by fiveninths to get 37 degrees Celsius.

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 Celsius to Fahrenheit: Tf = ((9/5)*Tc)+32
 For example, to convert a Celsius temperature of 100 degrees into
degrees Fahrenheit, first multiply the Celsius temperature reading by
ninefifths to get 180. Then add 32 to 180 and get 212 degrees
Fahrenheit.

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 Scientists use the Kelvin scale, which is based on the Celsius scale,
but has no negative numbers. Zero on the Kelvin scale is considered to
be absolute zero; that is, the point at which all molecular motion
stops.
 To convert a temperature reading into degrees Kelvin, simply add 273.16
to the Celsius temperature.
 The absolute zero version of the Fahrenheit scale is the Rankine scale.
Add 460 degrees to Fahrenheit temperatures to obtain the Rankine
temperature.

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 The linear thermal coefficient expansion coefficient a is an indication
of how much an object expands when heated and generally applies to
metals.

22

 Temperature of an icewater mixture is defined as 0º C
 This is the freezing point of water
 Temperature of a watersteam mixture is defined as 100º C
 This is the boiling point of water
 Distance between these points is divided into 100 segments

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 When the pressure of a gas goes to zero, its temperature is –273.15º C
 This temperature is called absolute zero
 This is the zero point of the Kelvin scale
 To convert: T_{C }= T_{K} – 273.15

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 Temperature readings are nearly independent of the gas
 Pressure varies with temperature when maintaining a constant volume

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 All gases extrapolate to the same temperature at zero pressure
 This temperature is absolute zero

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 Defined in terms of two points
 Agreed upon by International Committee on Weights and Measures in 1954
 First point is absolute zero
 Second point is the triple point of water
 Triple point is the single point where water can exist as solid,
liquid, and gas
 Single temperature and pressure
 Occurs at 0.01º C and P = 4.58 mm Hg

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 Some representative Kelvin temperatures
 Note, this scale is logarithmic
 Absolute zero has never been reached

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 The thermal expansion of an object is a consequence of the change in the
average separation between its constituent atoms or molecules
 At ordinary temperatures, molecules vibrate with a small amplitude
 As temperature increases, the amplitude increases
 This causes the overall object as a whole to expand

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 Thermostats
 Use a bimetallic strip
 Two metals expand differently

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 Pyrex Glass
 Thermal stresses are smaller than for ordinary glass
 Sea levels
 Warming the oceans will increase the volume of the oceans

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 At the temperature of water increases from 0ºC to 4 ºC, it contracts and
its density increases
 Above 4 ºC, water exhibits the expected expansion with increasing
temperature
 Maximum density of water is 1000 kg/m^{3} at 4 ºC

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 A gas does not have a fixed volume or pressure
 In a container, the gas expands to fill the container
 Most gases at room temperature and pressure behave approximately as an
ideal gas

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 Collection of atoms or molecules that move randomly
 Exert no longrange force on one another
 Occupy a negligible fraction of the volume of their container

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 It’s convenient to express the amount of gas in a given volume in terms
of the number of moles, n
 One mole is the amount of the substance that contains as many particles
as there are atoms in 12 g of carbon12

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 The number of particles in a mole is called Avogadro’s Number
 N_{A}=6.02 x 10^{23} particles / mole
 The mass of an individual atom can be calculated:

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 Boyle’s Law
 At a constant temperature, pressure is inversely proportional to the
volume
 Charles’ Law
 At a constant pressure, the temperature is directly proportional to the
volume
 GayLussac’s Law
 At a constant volume, the pressure is directly proportional to the
temperature

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 Robert Boyle discovered a relationship between the pressure and volume
of a gas. P_{1}V_{1}
= P_{2}V_{2}
 Volume varies inversely with change in pressure.

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 Correct the volume of gas from the indicated pressure to standard
pressure: 952 cubic cm at 86.4
kPa.
 P_{1}V_{1} = P_{2}V_{2}
 86.4 kPa (952 cm^{3}) = 101.325 kPa (V_{2})
 82252.8 cm^{3 }= 101.325 (V_{2})
 V_{2 }= 811.8 cm^{3}

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 A 225 cm^{3} volume of gas is collected at 57 ^{o}C. What volume would this sample of gas
occupy at standard temperature?
 V_{1} = V_{2}
225 cm^{3 }= V_{2}

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 Joseph GayLussac discovered the relationship between pressure and
temperature of a gas. P_{1 }=
P_{2}

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 Summarizes Boyle’s Law, Charles’ Law, and GuyLussac’s Law
 PV = n R T
 R is the Universal Gas Constant
 R = 8.31 J / mole K
 R = 0.0821 L atm / mole K

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51

 1. Calculate the volume, in
liters, occupied by each of the following:
 a. 2 mol H at 300 K & 1.25
atm
 b. .425 mol of ammonia at 37^{O}
C & 550 mm of Hg (760 mm = 1 atm)
 c. 4 g O at 57^{O } C & 675 mm Hg

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 2. Determine the number of moles
of gas contained in each of the following:
 a. 1.25 L at 250 K & 1.06 atm
 b. .80 L at 27^{O} C and
.925 atm
 c. 750 ml at 50^{O} C
& 700 mm

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 3. Calculate the pressure in
atmospheres (atm) exerted by each of the following:
 a. 2.50 L of HF containing 1.35
mol at 320 K
 b. 4.75 L of NO_{2}
containing .86 mol at 300 K
 c. 750 ml of CO_{2}
containing 2.15 mol at 57^{O} C

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 Remember, the number of molecules contained in one mole of any gas is
Avogadro’s numbers, N_{A}= 6.02 x 10^{23}
 So n = N/N_{A}, where n = no. of moles and N is the number of
molecules in the gas.
 Therefore PV = nRT= N/N_{A}RT and
 P V = N k_{B} T
 k_{B} is Boltzmann’s Constant
 k_{B} = R / N_{A} = 1.38 x 10^{23} J/ K
 This equation will allow us to relate the temp. of a gas to the average
kinetic energy of particles in the gas.

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 Equal volumes of gas at the same temperature and pressure contain the
same numbers of molecules
 Corollary: At standard
temperature and pressure, one mole quantities of all gases contain the
same number of molecules
 This number is N_{A}
 Can also look at the total number of particles: N = n N_{A}

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

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 The molecules interact only by shortrange forces during elastic
collisions
 The molecules make elastic collisions with the walls
 The gas under consideration is a pure substance, all the molecules are
identical

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 The pressure is proportional to the number of molecules per unit volume
and to the average translational kinetic energy of a molecule

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

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 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

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 Expressed as the rootmeansquare (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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