Pure Substances Part 1

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Pure Substances -- Part 1

• Physics 313
• Professor Lee Carkner
• Lecture 20

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Substances

• A substance can exist as solid, liquid, gas or in
  a combination
• A pure substance is either
• Composed of a single element
• A homogenous mixture of several elements
• Phases depend on P, V and T
• PV and PT diagrams produce curves separating
  phases
• PVT diagrams have surfaces as boundaries

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PV Diagram

• The phase of a substance depends on its position
  on the PV diagram
• Phases can only exist in certain areas
• Each point on the PV diagram represents
• P, V, T
• A phase or mixture of phases

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Saturation

• At saturation liquid and gas phases coexist
• The substance has to be at the saturation
  temperature for the pressure (or visa versa) in
  order to change phase
• Saturation curves define boundaries of liquid
  vapor mixture region

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Critical Point

• Where the saturation curves intersect is the
  critical point
• Critical point is on the critical isotherm
• At temperatures higher than this there is no
  distinction between liquid and gas
• Densities of both are the same

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PT Diagram

• Three curves can be drawn on the PT diagram
• Fusion curve
• solid and liquid co-exist
• Vaporization curve
• liquid and gas coexist
• Sublimation curve
• solid and gas coexist
• Juncture of the three curves is the triple point
  where all three coexist

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Other PT Features

• An isobar at standard atmospheric pressure
  intersects the normal boiling and melting points
• The critical point is on the vaporization curve
• Distinction between gas and liquid regions break
  down past this point

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Triple Points

• The triple point is a triple line on a PV diagram
• Different solid phases are possible
• May have different structures
• Called polymorphs
• Most exist at extreme T or P
• Triple point is a point where any three phases
  coexist
• Substance can have multiple triple points

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PVT Diagram

• P, V and T relations can be formed to create a
  three dimensional diagram
• Surfaces define volume regions where phases are
  allowed
• The PT and PV diagrams are formed by projection

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Equations of State

• Many equations of state are needed to express all
  of the relationships on a PVT diagram
• The ideal gas law holds for low pressures
• Other gas equations of state hold for standard
  pressures (van der Waals etc.)

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Finding Critical Point

• What defines the critical point
• Due to the shape of the isotherm we can say (at T
  TC)
• (dP/dV) 0
• (d2P/?V2) 0
• This gives three equations in three unknowns to
  solve for TC, PC, VC

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Molar Heat Capacity

• Heat capacity at constant pressure can be found
  by heating a sample at a uniform rate at constant
  pressure
• How do the heat capacities of solids vary from 0
  to 300 K?
• Consider molar heat capacity
• CP for one mol
• cP is zero at absolute zero and rises with T

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Debye Temperature

• For 1 mol of a solid a certain number of atoms
  will be vibrating in the crystal lattice
• Order solids by number of vibrating atoms
• At the Debye temperature cP is about 3R per NA of
  vibrating atoms
• cP falls rapidly below Debye temperature