BIOE 332

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BIOE 332

• The First Law of Thermodynamics
• January 21st, 2005

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Recap of Gas Properties

• Gases are ideal at high temperature and low
  pressures
• Deviations in ideality accounted for by different
  equation of state (e.g. van der Waals) that
  accounts for intermolecular forces
• Beyond critical temperature, supercritical
  fluids have technological applications

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Phase Transition
Experimental isotherms of carbon dioxide at
several temperatures. The critical isotherm',
the isotherm at the critical temperature, is at
31.04 ?C. The critical point is marked with a
star. Critical pressure pc Critical molar
volume
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From Gases to Biology Surfactant Molecules
Surfactant molecules are a surface-active
substances examples detergent In aqueous
solutions, they will partition to the surface
(also called the interface -- the boundary
between two phases) Ex Air-water
interface Generally have both polar and nonpolar
regions
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Membranes are composed of amphiphilic molecules
(phospholipids)
Alcohol
polar head group
Glycerol
Phosphate
Fatty acid
Fatty acid
nonpolar hydrocarbon tail
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Monolayer Compression Experiments
Wilhelmy Plate
Computer interfaced barrier for compressing
Teflon Langmuir trough
Subphase

• Insoluble (phospholipid ) monolayer is
  characterized by surface pressure, p

p go - g
go clean surface tension g surface tension of
surface with adsorbed amphiphiles

• Insoluble monolayers may be compressed by
  barriers sweeping the interface, allowing p to be
  easily manipulated

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Monolayer Penetration Experiments
understanding the interactions between adsorbed
molecules

• When a lipid monolayer is spread on a subphase
  containing a soluble component , the
  molecule will adsorb if it is surface active, has
  attractive interactions with the monolayer, or
  both.

change in surface pressure p Dp
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Effect of Salicylate on SOPC Isotherm
at 70 Å2
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Question

• What would the isotherm look like if the
  surfactant molecule underwent a phase transition
  during compression?

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State Functions
Relationship holds when dy is an exact
differential The function y is then a state
function The second cross partial derivatives are
equal ? Leads to the Maxwell Relations
Read Math Chapter D and handout !!!!
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Review Classes of Systems
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Review Types of Boundaries
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Endothermic process Absorbs energy or heat
temperature falls Example vaporization of water
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Exothermic process Release energy as heat
temperature rises Example combustion reaction
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Combined Processes
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Molecular Picture of Heat

• Heat chaotic molecular motion
• Thermal motion
• Boltzmann thermal energy of kT becomes
  fundamental in a number of processes
• -- gives limit on which biological signals can be
  detected and transmitted

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Molecular Picture of Work
Work organized motion Ex all atoms part of a
weight that is being raises F0/F1 ATPase turns in
mitochondria, flagellar motor in bacteria
molecules acting in concert Doing work is
equivalent to raising a weight see Sect. 5.1
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Evidence of Relation Between Heat and Work

• Contraction of a rubber band by heat
• Joules experiment
• -- Joule was a brewer in Manchester, England
• Showed equivalence of heat and mechanical energy

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The First Law

• Internal energy U
• (total kinetic and potential energy of molecules
  in the system)
• DU Uf - Ui is a state function
• DUqw
• dU dqdw
• Heat and work are equivalent ways of changing
  systems energy

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What confuses everyone

• Conventions on the sign of q and w
• work done on a system is positive
• work done by a system is negative
• heat transferred to a system is positive
• heat transferred out a system is negative
• Steam engine takes in heat, puts out work

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Path Independence
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Question

• What does the First Law say about the internal
  energy of an isolated system?

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Expansion Work
When a piston of area A moves out through a
distance dz, it sweeps out a volume dV A dz.
The external pressure, pex, is equivalent to a
weight pressing on the piston, and the force
opposing expansion is F pex A.
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Other Types of Work

• Surface Expansion
• Surface tension and change in interfacial area
• Very important concepts in biomaterials, lipid
  membranes
• dUsurf g dA
• Electrical
• Movement of electric charge in a potential field
• dUq ydq

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Expansion Against Constant Pressure
The work done by a gas when it expands against a
constant external pressure, pex, is equal to the
shaded area in this example of an indicator
diagram.
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Reversible Expansion of Perfect Gas
The work done by a perfect gas when it expands
reversibly and isothermally is equal to the area
under the isotherm p nRT/V. The work done
during the irreversible expansion against the
same final pressure is equal to the rectangular
area shown slightly darker. Note that the
reversible work is greater than the irreversible
work.
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Heat transactions

• At constant volume, system only capable of PdV
  work
• dU dq
• or DUqV
• gives us way to measure change in the internal
  energy measure heat produced

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Bomb Calorimeter
A constant-volume bomb calorimeter. The bomb' is
the central vessel, which is massive enough to
withstand high pressures. The calorimeter (for
which the heat capacity must be known) is the
entire assembly shown here. To ensure
adiabaticity, the calorimeter is immersed in a
water bath with a temperature continuously
readjusted to that of the calorimeter at each
stage of the combustion. q CDT
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Importance to Biology

• Differential Scanning calorimetry
• -- used to measure membrane phase transitions
• -- protein unfolding
• -- RNA/DNA unfolding

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Heat Capacity
Molar heat capacity Specific heat capacity
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Coming next Enthalpy