Critical Point Drying

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Critical Point Drying

1. Biological specimens
2. MEMS
3. Aerogels
4. Spices

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Single film annealed 16 stages
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Single film annealed 16 stages
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Scaling collapse for indicated values of R0
(metallic side, recall Rc22.67 k?)
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Measurement of Irreversible magnetization

• Field cooled (MFC) and Zero field cooled (MZFC)
  magnetization.
• ?M(H,T) MFC(H,T) MZFC(H,T) , is the
  irreversible magnetization

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Field dependence of ?M(H,T) isotherms
Ni/AlOx multilayers
Increasing T
Hm(T) ? Magnetic field where maxima of
?M occures ?Mmax(T) ? Maximum value of ?M
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Scaling collapse of ?M
Ni/AlOx multilayers
T
(T)
?M (H,T) ?Mmax(T)F(H/Hm)
(T)
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Scaling collapse in other materials
Zotev , Orbach et. all, PRB, 2002
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Hydrogen Molecules (Quadrapolar Glass)
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The combined 1st and 2nd Laws
The 2nd law need not be restricted to reversible
processes

• dQ is identifiable with TdS, as is dW with PdV,
  but only for reversible processes.
• However, the last equation is valid quite
  generally, even for irreversible processes,
  albeit that the correspondence between dQ TdS,
  and dW PdV, is lost in this case.

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Conversion of Heat to Work (a heat engine)
Heat reservoir at temperature T2 gt T1
Q ? heat W ? work both in Joules
Q2
Heat Engine
Q1
Heat reservoir at temperature T1 lt T2
Dont confuse with Joule-Thomson coefficient
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The combined 1st and 2nd Laws
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Work and Internal Energy

• Differential work dW is inexact (work not a state
  variable)
• Configuration work is the work done in a
  reversible process given by the product of some
  intensive variable (y) and the change in some
  extensive variable (X).
• dW is the work done on the system, e.g. dW is
  positive when a gas contracts.
• Dissipative work is done in an irreversible
  process and is always done on the system, i.e.
  dWirr gt 0 always.
• Total work (configuration and dissipative) done
  in adiabatic process between two states is
  independent of path. This leads to the definition
  of internal energy (state variable).

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Equation of State of an Ideal Gas

• In chapter 1, we used the zeroth law to show that
  a relationship always exists between P, V and T.

General form f (P,V,T) 0 Example PV nRT
(ideal gas law)
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Equation of State of a Real Gas
Van der Walls equation in intensive form
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London van der Waals interaction
Etotal K V constant

• So, the addition of particles to a system results
  in the addition of kinetic energy to the system
  which almost immediately dissipates to the entire
  system.
• Therefore, the addition of particles changes the
  internal energy of the system. The change in the
  internal energy dU is proportional to the number
  of particles dn that are added. The
  proportionality constant m is called the
  chemical potential.

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Properties of Heat
It is the temperature of a body alone that
determines whether heat will flow to or from a
body,
Heat energy is transferred across the boundary
of a system as a result of a temperature
difference only.
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Heat Capacity and specific heat
The heat capacity C of a system is defined as
The specific heat capacity c of a system is

• Specific heat is obviously an intensive quantity.
• SI units are J.kilomole-1.K-1.

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Heat Capacity and specific heat
Because the differential dq is inexact, we have
to specify under what conditions heat is added.

• the specific heat cv heat supplied at constant
  volume
• the specific heat cP heat supplied at constant
  pressure

Using the first law, it is easily shown that

• For an idea gas, the internal energy depends only
  on the temperature of the gas T. Therefore,

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The Gay-Lussac-Joule Experiment

• Suggests an experiment measure temperature
  change of a gas as a function of volume whilst
  keeping u fixed this will enable us to determine
  how u depends on v.

The Joule coefficient

• For an ideal gas

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Expansivity and Compressibility
Two important measurable quantities
Expansivity
Compressibility
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The Second Law of Thermodynamics

• Clausius statement It is impossible to
  construct a device that operates in a cycle and
  whose sole effect is to transfer heat from a
  cooler body to a hotter body.

• Kelvin-Planck statement It is impossible to
  construct a device that operates in a cycle and
  produces no other effect than the performance of
  work and the exchange of heat from a single
  reservoir.
• Carnots theorem No engine operating between two
  reservoirs can be more efficient than a Carnot
  engine operating between the same two reservoirs.

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The Clausius Inequality and the 2nd Law
Consider the following cyclic process
P
2
Irreversible
Reversible
1
V
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The Clausius Inequality and the 2nd Law
The Clausius inequality leads to the following
relation between entropy and heat
This mathematical statement holds true for any
process. The equality applies only to reversible
processes.
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The Carnot Cycle

1. a?b isothermal expansion
2. b?c adiabatic expansion
3. c?d isothermal compression
4. d?a adiabatic compression

1. W2 gt 0, Q2 gt 0 (in)
2. W' gt 0, Q 0
3. W1 lt 0, Q1 lt 0 (out)
4. W'' lt 0, Q 0

• Stirlings engine is a good approximation to
  Carnots cycle.

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Cooling via Work (a Refrigerator)
Environment at temperature T2 gt T1
Q2
Refrig- erator
Q1
Refrigerator Inside, temperature T1 lt T2
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Available energy
T2 gt T1
dQ
Available energy in a reversible cycle
M
dW
(1 T1/T2)dQ
Unavailable energy
T1dQ/T2
T1 lt T2
There exists no process that can increase the
available energy in the universe.
Efficiency h
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Entropy changes in reversible processes
Various cases

• For an ideal gas quite generally

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Entropy changes in reversible processes
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Entropy changes in reversible processes
Various cases

• Isochoric process We assume u u(v,T) in
  general, so that u u(T) in an isochoric
  process. Therefore, as in the case for an ideal
  gas, du cvdT. Thus,

provided cv is independent of T over the
integration.
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Entropy changes in reversible processes
Various cases

• Isothermal (and isobaric) change of phase

where l is the latent heat of transformation.
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Entropy changes in reversible processes
Various cases

• Isothermal (and isobaric) change of phase

where l is the latent heat of transformation.
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Entropy changes in reversible processes
Various cases

• Isobaric process More convenient to deal with
  enthalpy

h h(P,T) in general, so that h h(T) in
isobaric process.
provided cP is independent of T over the
integration.
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The Tds equations
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The Joule-Thomson Experiment
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Enthalpy
When considering phase transitions, it is useful
to define a quantity h called enthalpy

• Because h depends only on state variables, it too
  must be a state variable hence its usefulness.

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Enthalpy and specific heat

• The specific heat is not defined at any phase
  transition which is accompanied by a latent heat,
  because heat is transferred with no change in the
  temperature of the system, i.e. c 8.
• However, enthalpy turns out to be a useful
  quantity for calculating the specific heat at
  constant pressure

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The Gibbs function And Chemical Potential
Using Eulers theorem, one can now define an
absolute value for the internal energy of a system
Thermal (kinetic)
Chemical (potential)
Mechanical (potential)
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Enthalpy
When considering phase transitions, it is useful
to define a quantity h called enthalpy

• Because h depends only on state variables, it too
  must be a state variable hence its usefulness.

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Enthalpy and Pressure

• Thus, we see the connection between the physics.
• The main difference is that enthalpy is relevant
  during constant pressure processes, whereas
  internal energy is relevant during constant
  volume processes.

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The Tds equations