Physics 160, April 4, 2006

1
Physics 160, April 4, 2006

• In the news
• More energy and thermodynamics basics
• - Reaction theory
• - 1st and 2nd Laws of Thermodynamics
• - Efficiency
• - Entropy
• First debate groups and topics

2
In the newsenergy, global warming

• Hybrid cars less energy efficient, says study
• (http//www.thestandard.com.hk/news_detail.asp?pp_
  cat17art_id15821sid7367550con_type1)
• Bipartisan plans look to cut greenhouse gas
  (http//www.sacbee.com/content/politics/story/1423
  8609p-15058990c.html)

3
Energy mostly from burning fuelReaction
theory
4
Schematic of Reactions (Chemical or nuclear.)
Must supply energy to overcome barrier
5
More on reactions

• Energy release typically measured as heat of
  combustion here are some relevant numbers for
  chemical reactions
• Heat of combustion is an intrinsic property of a
  fuelenergy barrier depends upon environment

6
Reaction Barriers

• Generically, under thermal conditions only, rate
  of activation over the barrier goes as
• exp(-EB/kBT)
• where kB 1.38 x 10-23 J/mole-K is
  Boltzmanns constant, and the temperature T is
  measured in absolute (Kelvin) units.
• Hydrogen as a chemical fuel low barrier to
  activation (small match!) SAFETY ISSUE!
• Hydrogen as a nuclear fuel (fusion) HUGE BARRIER
  due to Coulomb repulsion between positively
  charged Hydrogen nuclei.
• Catalysts Reduce barrier height without
  changing energy release. This is usually
  accomplished by reducing the reaction
  dimensionalitycatalysts (enzymes) in the
  biological context can thereby increase reaction
  rates by as much as 1020!!!!!

7
Basic law of hydrocarbon reactions

• Natural gas CH4, Oil CH2, Coal CH
• For every hydrocarbon burned, approximately one
  carbon dioxide is released
• CH4 2 O2 ? CO2 2 H2O
• 2 CH2 3 O2 ? 2 CO2 2 H2O
• 4 CH 5 O2 ? 4 CO2 2 H2O
• In atmosphere with more than Oxygen, other
  products possible
• ? Release of CO2 into atmosphere from burning of
  fossil fuels is unavoidable

8
Estimating the characteristic energy in a
chemical bond

• Factoid One barrel (bbl) of oil has about 6
  billion Joules of energy and 42 gallons of oil.
  One gallon is about 4 liters, or about 4000 cm3
• Oil is approximately CH2, which has a molar mass
  of 14 grams or 0.014 kg.
• Oil is lighter than waterthe density is about
  70 of H2O, or about 0.7 g/cm3
• Hence, one barrel of oil has about .7g/cm3 x 4000
  cm3/gallon x 42 gallons 118000 g, which is
  118000 g/(14 g/mole) 8400 moles 8400 moles x
  6.02 x 1023 molecules/mole 5.1 x 1027
  molecules. That means the energy released per
  molecule on burning oil is 6 x 109 J/(5 x 1027
  molecules) 1.2 x 10-18 J/molecule 7.3
  eV/molecule.

9
Laws of Thermodynamics

• First Law DQ DU W
• Heat change in process change in internal
  energy plus work done
• Energy is conserved
• Second Law
• (Version 1) The entropy of a closed system will
  always increase or remain constant under any
  process.
• (Version 2) No heat engine, operating between
  high temperature TH and low temperature Tc can
  have an efficiency h exceeding 1 Tc/TH which is
  the efficiency of a Carnot engine operating
  between those two temperatures. (Efficiency of a
  heat engine is defined as Wout/QH, where Wout is
  the work done by the engine and QH is the heat
  taken in at higher temperature.)
• Increasing Entropy is the Arrow of Time

10
Heat capacity measures temperature rise for
given heat input

• Energy goes into exciting additional motionfor
  most materials, this is dominated by the
  vibrational energy OR by the kinetic energy
  (gases, liquids)
• Property of materialcan be defined on per unit
  mass or per mole basis.
• Per mass dQ added heat, dT temp. change
• c (1/m) dQ/dT
• Water, solids high heat capacity Air/gases
  low heat capacity. Thermal inertia

11
Efficiency of Thermal Engines
12
Question to ponder with your neighbors

• You are working out in the ARC gym on an
  elliptical trainer machine. You are paying
  attention to the readouts as you exercise.
• a) You notice that you burn 1200 Cal/hour
  while you produce 300 Watts according to the
  readout. Noting that both these numbers are
  units of energy per unit time or power, you seek
  to compare them. Are they the same? If not, why
  not (ie, what does each measure)?
• b) Can you use these numbers to estimate your
  efficiency as an electrical power plant on
  the elliptical trainer? For comparison, typical
  automobile engines are about 25 efficient in
  converting fuel energy to mechanical work, and
  coal/nuclear plants are about 30-35 efficient in
  converting heat from fuel to electrical energy.

13
Discussion

• 1300 Cal/hr 1300 x 4.18 x 103 J/hr x (1
  hr)/(3600 sec) 1390 Watts 300 Watts!
• We conclude that the 1300 Cal/hr is what you burn
  internally while 300 Watts is what you produce
  mechanically
• Efficiency is Energy Out/Energy In 300/1390
  22
• This is comparable to internal combustion
  engines, low compared to electrical power plants
  (30-40)

14
Power Plant
15
Statistical Definition of Entropy

• For a system with W states, Boltzmann showed
  that the entropy per molecule S is given by
• S kB lnW
• where kB 1.38 x 10-23 J/K is Boltzmanns
  constant and ln(x) is the natural logarithm (base
  e) of x. In this picture, an open system tends
  to the maximum of entropy, and this is expressed
  in the thermodynamic Free Energy G given by
• G U TS
• where U is the internal energy and T is the
  temperature. Thermodynamic stability is implied
  by lower free energy, which can be achieved by
  decreasing U (through, e.g., increased atomic
  bonding in say a crystal vs. a liquid) or
  increasing S (through increasing disorder in say
  a liquid vs. a solid). At a phase change of
  discontinuous type such as melting, the free
  energy difference between the phases is zero.
  Notice that at lower T, the free energy can be
  lowered by increasing order (lowering U) more
  than disorder (increasing S).

16
Entropy Example Books in two rooms

• Assume you and your housemate are taking the same
  courses and you have purchased the relevant N
  textbooks, while your housemate has not.
  Initially, all books are in your room, but at
  time t0, your roommate starts bringing books to
  their room, randomly moving them back and forth.
  
• This is a system with 2N total states since
  each book can be either in your room or the
  housemates room.

17

• The probability PN(m) of finding m books in your
  room is the number of ways to select m objects
  out of N total divided by the total number of
  states, ie
• PN(m) 2-N N!/(N-m)!m!
• where N! N(N-1)(N-2)..(2)(1) is N
  factorial
• Hence, for six books we obtain the table

18
N10 books
N36 books

• Above are plots of PN(m) (with lines between the
  points) for N10,30.
• Notice that the tendency with increasing N is for
  the probability distributions become more sharply
  peaked about N/2indeed for very large N the
  width goes as N1/2 so that the width to peak
  ratio goes to zero as 1/N1/2, and the maximum
  entropy principle is clear as a statistical law
  for large numbers of thingsin this case, books.
• Notice that it takes energy to reorder the books!
  You would supply that energy and while you
  decrease the entropy of the books, you would
  increase the entropy of the universe through the
  waste heat you produce in the process.

19
Initial book distribution
Prob in your room
N10 books
Books in your room
Prob in your room
Prob in your room
N36 books
N20 books
Books in your room
Books in your room
20
Debate Topics

• Directions Spend about 30-60 minutes researching
  these topics between now and Thursday. Each
  group will be given about 15 minutes in class on
  Thursday to prepare.
• For the last 16 years there has been a battle to
  open the Arctic National Wildlife Refuge for oil
  drilling. If you were A you must argue pro ANWR
  drilling, B you must argue against.
• The state of Oregon has plans to replace the tax
  per gallon of gasoline you buy in the state by a
  tax on the miles you drive within the state. If
  you are C you must argue pro mileage tax, and if
  you are D you must argue against it.

21
Debate Format

• 5 minutes presentation
• 4 minutes discussion between
• 3 minutes rebuttal
• (15 minutes prep before debates)