MBB 323

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MBB 323

• Lecture 3
• Office hours Friday 230
• Tutorials start this week.

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Summary from last lecture

• A system is defined by its boundary.

• The total energy found in the system and its
  surroundings does not change.

• Energy can take a variety of forms.
• Energy has the unit of Joules (J) kgm2/s2
• Last lecture discussed gravitational and
• kinetic energy doing a certain amount of work
• per second on a pump (Power measured in
• Watts W J/s).

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Farmer can pump water to his field if
(Ain-Aout)/ Aout hout /hdrop
V (m/s)
The pump system
To field
Aout (m2)
hout (m)
V (m/s)
V (m/s)
From valley stream
hdrop (m)
Ain (m2)
Ain - Aout (m2)
Check out www.agr.gc.ca/pfra/water/wpower_e.htm
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WORK energy can be converted completely into
other forms of WORK

• Forms of WORK
• Mechanical lt-gt Electrical (A generator)
• Electrical lt-gt Mechanical (A motor)
• Gravitational lt-gt Mechanical (A hydro dam)
• Review carefully these forms of energy.

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WORK energy can be converted completely into HEAT

• Mechanical -gt Heat (Stirring a liquid, friction)
• Electrical -gt Heat (A kettle)
• Gravitational -gt Heat (a water fall)
• For a closed system (which means?) the change in
  energy of a system is
• DE w q,
• w the work done on the system.
• q the heat flowing into the system.
• Other terms if particle flow is possible (see
  demo).
• Heat is a form of low grade energy. To
  understand what heat really is we need to first
  discuss temperature.

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Introduction to Temperature

• When two systems are allowed to exchange heat,
  they will eventually reach the same temperature.
• Heat is positive if it flows into a system (here
  from the hotter system into the colder).
• Heat is negative if it flows out of a system.
• A new principle is being satisfied here. It is
  not a conservation law, but rather a law of
  maximization. As we shall see this has
  everything to do with entropy.

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Measuring Temperature

• A thermometer is used to measure temperature.
• A thermometer can take many forms
• Mercury or other liquid in a bulb connected to a
  thin evacuated glass tube.
• Thermocouple
• Gas thermometer (PV nRT).
• Colour (see Stefans law p 27)
• Recently developed a primary thermometer based
  on quantum mechanics Spietz et al., Science,
  Vol 300, p1929

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The Fahrenheit system (1724)

• "placing the thermometer in a mixture of sal
  ammoniac or sea salt, ice, and water a point on
  the scale will be found which is denoted as zero.
  A second point is obtained if the same mixture
  is used without salt. Denote this position as
  30. A third point, designated as 96, is obtained
  if the thermometer is placed in the mouth so as
  to acquire the heat of a healthy man." (D. G.
  Fahrenheit,Phil. Trans. (London)

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The Celsius system (1742)

• Celsius scale defines as 0 degrees as the
  temperature of the triple point of water (mixture
  of ice, water and steam at atmospheric pressure
  101.325 kPa) and 100 degrees as the boiling point
  of water at this pressure. Originally Celsius
  defined the scale the other way around, but this
  was soon dropped in favour of the current scale.
• There is nothing special about this scale except
  that water is commonly found and that the
  gradations are a useful size.

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The Kelvin Scale (1848)

• Defines absolute zero and is the scale to use for
  thermodynamic problems.
• The Kelvin Scale has exactly the same slope as
  the Celsius scale. This means that relative
  changes in temperature are the same between the
  two scales.
• -i.e. 100 degrees Celsius or Kelvin between
  freezing and boiling points of water.
• -generally T aTb (C-gtK a1, b273.15)
• -What would be the conversion between C-gtF?
• Absolute zero -273.15 degrees centigrade.
• Boiling point of liquid nitrogen 77K, liquid
  helium 4.2K.

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Why do we need an absolute zero?

• Quantum mechanically there is a lowest energy
  state for any given system.
• This state is called the ground state.
• A temperature of zero corresponds to finding a
  system only in its ground state.
• As we will see later temperature is related to
  the change in the energy of a system as the
  number of states varies. (Entropy 2nd law)
• Properties of gases that are close to ideal
  suggest a lowest temperature.

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Avogadros Number

• How would you measure it? Consider that this is
  one of the most uncertain physical constants.
• NA 6.023 x 1023 particles.
• PVnRT (Pressure in Pascals, Volume in cubic
  meters, n number of moles, R8.314 JK -1 mol-1,
  T in Kelvin.
• PV NkT, same as above, but N is number of
  particles, and k is Boltzmanns constant 1.318
  x 10-23 JK -1 (see p79).
• Measure the volume and mass of a pure substance
  in a crystal form. Then determine the exact
  lattice spacing by X-ray crystallography.

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Heat Capacity

• What temperature change occurs when heat is
  deposited in a system?
• The easiest way to deposit heat is to use
  electrical resistance.
• Use an adiabatic closed system, monitor
  temperature as a function of heat energy
  deposited.
• dq/dT C(T), normally specified at constant P or
  V.
• This is the heat capacity of the system, its
  normally a good idea to consider a molar heat
  capacity (the heat capacity you would observe if
  one mole of the system was used). i.e C(T)
  nC(T), where n is the numer of moles in the
  system. This normally value is normally written
  with an overline.
• Molar Heat capacity for
• ice 38.07 JK-1mol-1,
• water 75.24 JK-1mol-1 (see p37)
• For a substance like water (pure), heat
  capacities can become singular at phase
  transitions (ice -gt water -gt steam). These
  values are called latent heats (p45) and can be
  quite large.
• Macromolecular phase transitions however are much
  broader (and what we care about more).
• Consider the melting of a DNA oligonucleotide.

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A picture of the physical state of a system
something to think about.

• Volume of 1 Mole of water at room temp and
  pressure?
• 1Mole of water at atmospheric pressure and at
  room temperature occupies 18 ml of volume (as
  density is 1 g/ml, MW is 18g/Mole).
• What is the average spacing between liquid water
  molecules?
• 6.02 x 1023 molecules occupy 18 x 10-6 m3 so on
  average one molecule occupies 3 x 10-29 m3. The
  dimensions of this box would be 3 x 10-10 m.
• How about of 1 Mole of steam under the same
  conditions?
• PVnRT gt 101.3 x 103 V 8.31 (298) m3
• V 0.024 m3 , so now each molecule occupies on
  average volume of 4 x 10-26 m3, or a cube having
  edges 3.4 X 10-9 m long.
• Why does nature favour under these conditions
  liquid water and not steam? Consider also that
  the water and steam in this example has the same
  average kinetic energy of 3/2kT or 600m/s.

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Next Class

• Variables and equations of state (p29-44)
• Read closely about the work done by pressure or
  volume changes (p21-23).
• Read about reversible and irreversible processes
  (p33-36)
• Read the heat capacity section (p25-27).