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Critical Point Drying

Critical Point Drying. Biological specimens MEMS Aerogels Spices. Single film annealed: 16 stages. Single film annealed: 16 stages. Scaling collapse for indicated values of R 0 (metallic side, recall R c =22.67 k  ). Measurement of Irreversible magnetization.

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Critical Point Drying

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  1. Critical Point Drying Biological specimens MEMS Aerogels Spices

  2. Single film annealed: 16 stages

  3. Single film annealed: 16 stages

  4. Scaling collapse for indicated values of R0 (metallic side, recall Rc=22.67 k)

  5. 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

  6. (Hm(T), ∆Mmax (T)) Field dependence of ∆M(H,T) isotherms Ni/AlOx multilayers Increasing T Hm(T)→ Magnetic field where maxima of∆Moccures ∆Mmax(T)→ Maximum value of ∆M

  7. Scaling collapse of ∆M Ni/AlOx multilayers T (T) ∆M(H,T) = ∆Mmax(T)F(H/Hm) (T)

  8. Scaling collapse in other materials Zotev , Orbach et. all, PRB, 2002

  9. Hydrogen Molecules (Quadrapolar Glass)

  10. The combined 1st and 2nd Laws The 2nd law need not be restricted to reversible processes: • đQ is identifiable with TdS, as is đW with PdV, but only for reversible processes. • However, the last equation is valid quite generally, even for irreversible processes, albeit that the correspondence between đQ & TdS, and đW & PdV, is lost in this case.

  11. Conversion of Heat to Work (a heat engine) Efficiency (h*): Heat reservoir at temperature T2 > T1 Q heat W  work both in Joules Q2 Heat Engine Q1 Heat reservoir at temperature T1 < T2 *Don’t confuse with Joule-Thomson coefficient

  12. The combined 1st and 2nd Laws If more than one type of particle (constituent) is added, then

  13. Work and Internal Energy • Differential work đW 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). • đW is the work done on ‘the system’, e.g. đW is positive when a gas contracts. • Dissipative work is done in an irreversible process and is always done ‘on the system’, i.e. đWirr > 0 always. • Total work (configuration and dissipative) done in adiabatic processbetween two states is independent of path. This leads to the definition of internal energy (state variable).

  14. Equation of State of an Ideal Gas n quantifies the amount of the substance. The units of R and n are linked such that their product nR has the dimensions of joules/kelvin. • If n measured in kilomoles, then R = 8.314  103 J/kilomoleK • If n measured in moles, then R = 8.314 J/moleK • Ideal gas law may also be written in intensive form Pv = RT v is the specific volume in either m3/mole or m3/kilomole • 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)

  15. Equation of State of a Real Gas CP Van der Walls’ equation in intensive form:

  16. London – van der Waals’ interaction Thus, we need to modify the combined 1st and 2nd laws: dU = TdS – PdV + mdn Thermal (kinetic) Mechanical, chemical (potential) 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’.

  17. Properties of Heat • However, this does not necessarily imply that the transfer of heat to a body will increase its temperature. It may also undergo a change of state (phase) from e.g. a liquid to a gas, without a change in temperature. • Also, if the temperature of a system increases, it does not necessarily imply that heat was supplied. Work may have been done on the system. Therefore, “Heat is the change in internal energy of a system when no work is done on or by the system.” 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.”

  18. Heat Capacity and specific heat • Heat capacity is an extensive quantity. 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.

  19. Heat Capacity and specific heat Because the differential đq 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,

  20. 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:

  21. Expansivity and Compressibility Two important measurable quantities: Expansivity: Compressibility:

  22. 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. • Carnot’s theorem: No engine operating between two reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs.

  23. The Clausius Inequality and the 2nd Law Consider the following cyclic process: P 2 Irreversible Reversible 1 V

  24. The Clausius Inequality and the 2nd Law For an isolated system, đQ = 0, therefore This leads to the following statement: • The entropy of an isolated system increases in any irreversible process and is unaltered in any reversible process. This is the principle of increasing entropy. 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.

  25. The Carnot Cycle • ab isothermal expansion • bc adiabatic expansion • cd isothermal compression • da adiabatic compression • W2 > 0, Q2 > 0 (in) • W' > 0, Q = 0 • W1 < 0, Q1 < 0 (out) • W'' < 0, Q = 0 • Stirling’s engine is a good approximation to Carnot’s cycle.

  26. Cooling via Work (a Refrigerator) Coefficient of Performance (c): Environment at temperature T2 > T1 Q2 Refrig- erator Q1 Refrigerator Inside, temperature T1 < T2

  27. Available energy T2 > T1 đQ Available energy in a reversible cycle: M đW (1 – T1/T2)đQ Unavailable energy: T1đQ/T2 T1 < T2 There exists no process that can increase the available energy in the universe. Efficiency = h

  28. Entropy changes in reversible processes Various cases: • For an ideal gas quite generally:

  29. Entropy changes in reversible processes Various cases: • Adiabatic process: đqr = 0, ds = 0, s = constant. A reversible adiabatic process is isentropic. THIS IS NOT TRUE FOR AN IRREVERSIBLE PROCESS! • Isothermal process:

  30. 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.

  31. Entropy changes in reversible processes Various cases: • Isothermal (and isobaric) change of phase: where l is the latent heat of transformation.

  32. Entropy changes in reversible processes Various cases: • Isothermal (and isobaric) change of phase: where l is the latent heat of transformation.

  33. 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.

  34. The Tds equations

  35. The Joule-Thomson Experiment • Thus, a throttling process occurs at constant enthalpy. • The experiment then involves throttling the gas for different values of P2. If h depends on P, then T will change during a constant h throttling process (next slide). • This contrasts the previous experiment where the search was for a change in T during a constant u expansion.

  36. Enthalpy • When a material changes phase (e.g. from a solid to a liquid) at constant temperature and pressure, latent heat l must be added. This heat of transformation is related simply to the enthalpy difference between the liquid and solid 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.

  37. Enthalpy and specific heat • For an ideal gas, the enthalpy depends only on the temperature of the gas T. Therefore, • 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= ∞. • However, enthalpy turns out to be a useful quantity for calculating the specific heat at constant pressure

  38. The Gibbs function And Chemical Potential From this definition, one can easily show that From the above, one readily sees that m = G/nfor a system with only one constituent, i.e. m = g. This is not true for mixtures or multi-constituent systems. Using Euler’s theorem, one can now define an absolute value for the internal energy of a system Thermal (kinetic) Chemical (potential) Mechanical (potential)

  39. Enthalpy • When a material changes phase (e.g. from a solid to a liquid) at constant temperature and pressure, latent heat l must be added. This heat of transformation is related simply to the enthalpy difference between the liquid and solid 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.

  40. Enthalpy and Pressure The Joule-Thomson coefficient: • For an ideal gas: • 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.

  41. The Tds equations These equations give: • heat transferred (đq = TdS) in a reversible process; • the entropy by dividing by T and integrating; • heat flow in terms of measurable quantities; • difference in specific heat capacities, cP, b, k, T, etc..; • relationships between coordinates for isentropic processes.

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