Topic Summaries: Matter

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© 1998-2008 by Glenn Elert -- A Work in Progress
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  1. Matter
    1. The Atomic Nature of Matter
      • Ordinary matter (as opposed to dark matter) is mostly composed of atoms.
      • Atoms …
        • are discrete entities.
          • A discrete system is composed of distinct individual parts. A discrete system is separable into pieces.
          • The opposite of discrete is continuous. A continuous system forms an unbroken whole without interruption. One region blends seamlessly into another.
        • can only be found in a limited number of basic types called elements (short for chemical elements).
          • There are 90 naturally occurring elements found on earth.
          • An additional 28 elements have been produced artificially in laboratories on earth.
          • A few elements that exist on earth only in the laboratory have been detected in stars other than the sun.
        • can be stable or unstable.
          • Unstable atoms have a finite lifetime.
            • There is a statistical probability that an unstable atom will decay into an atom of a different element.
          • Stable atoms are eternal.
            • The stable atoms of everyday existence are several billion years old.
              • Nearly all of the hydrogen and helium in the universe was created in the first three minutes of the universe's existence (13.7 billion years ago).
              • Nearly all of the elements heavier than helium found on the earth were created many millions of years before the solar system formed (4.5 billion years ago).
            • Stable atoms can be used over and over again (recycled) in different combinations and will never "wear out".
        • can be "seen" only with great difficulty.
          • Atoms are effectively "invisible".
            • Atoms are on the order of 10−10 m in size.
            • Light waves are on the order of 10−6 m in size.
            • Since light is 10,000 times larger than atoms, atoms are too small to be "seen" with light. (No optical device can ever be used to image atoms.)
          • Atoms can be inferred to exist through …
            • the chemical laws of definite and multiple proportions.
            • the physical laws of statistical thermodynamics.
          • Atoms can be imaged through …
            • x-ray diffraction
            • scanning tunneling electron microscopy
            • atomic force microscopy
      • Atoms can combine to form …
        • ionic solids
        • network solids
        • metallic solids
        • molecules
    2. Chemical Potential Energy
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    3. Allotropes & Polymorphs
      • There are often several ways to arrange the particles of a substance.
      • These variations are called polymorphs or allotropes.
    4. Avogadro's Hypothesis
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    5. Density
      • Density is the ratio of mass to volume.
        • Density is a measure of a material's or object's compactness.
        • As a scalar quantity it has no direction.
        • Density is a way to describe mass in a continuous system
           
        ρ =  m
        V
           
      • Units
        • The SI unit of density is the kilogram per cubic meter [kg/m3].
        • The Gaussian unit of density is the gram per cubic centimeter which is equivalent to a gram per milliliter [1 g/cm3 = 1 g/ml].
        • One thousand kilograms per cubic meter equals one gram per cubic centimeter [1000 kg/m3 = 1 g/cm3].
      • Specific gravity is the ratio of the density of a substance to the density of a standard substance.
        • The standard substance is usually water for solids and liquids and air for gases.
          • The density of liquid water under typical conditions on earth is approximately 1000 kg/m3.
          • The density of air at room temperature near the surface of the earth is approximately 1.2 kg/m3.
        • Specific gravity is a unitless quantity.
  2. Phases
    1. Gases
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    2. Liquids
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    3. Solids
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    4. Glasses
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    5. Plasmas
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    6. Metals
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  3. Solids
    1. Elasticity
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    2. Scaling
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  4. Liquids
    1. Surface Tension
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    2. Capillarity
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  5. Fluids
    1. Pressure
      • Pressure is the ratio of normal force to area.
        • Although both force and area are vectors, pressure is a scalar quantity and has no direction.
        • Pressure is a way to describe force in a region of a continuous system.
         
        P =  F
        A
         
      • Units
        • The SI unit of pressure is the pascal [Pa = N/m2 = kg/ms2].
        • One hundred thousand pascals are sometimes called a bar [100,000 Pa = 1 bar].
        • The unit atmosphere is 101,325 Pa by definition.
      • Absolute vs. Gauge
        • The pressure of a region, as defined above, is its absolute pressure (P).
        • The pressure difference between a system and its environment (P0) is known as gauge pressure (Pg).
         
        P = P0 + Pg
         
    2. Pressure in a Fluid
      • Pressure in a fluid (P) at rest …
        • is equal to the weight of a column of fluid divided by the area on which it rests, so that it …
          • increases uniformly with depth (h)
          • is directly proportional to the density of the fluid (ρ)
          • depends on the surface pressure (P0)
           
          P = P0 + ρgh
           
        • acts equally in all directions and therefore …
          • exerts a net force perpendicular to any surface that it contacts
      • Pascal's principle: Pressure changes applied to the surface of an enclosed fluid are transmitted evenly throughout the fluid.
        • Hydraulics increase force, but
           
          P1 =  F1  =  F2  = P2
          A1 A2
           
        • decrease distance (since energy is conserved)
           
          W1 = F1s1 = F2s2 = W2
           
    3. Buoyancy
      • Buoyancy (also known as the buoyant force) is the force exerted on an object that is wholly or partly immersed in a fluid.
        • The symbol for the magnitude of buoyancy is B or FB
        • As a vector it must be stated with both magnitude and direction.
          • Buoyancy acts upward for the kind of situations encountered in everyday experience.
        • As with other forces, the SI unit of buoyancy is the newton [N].
      • Buoyancy is caused by differences in pressure acting on opposite sides of an object immersed in a static fluid.
        • A typical situation:
          1. The pressure on the bottom of an object is greater than the top
            (since pressure increases with depth).
          2. The force on the bottom pushes up and the force on the top pushes down
            (since force is normal to the surface).
          3. The direction of the net force due to the fluid is upward.
        • Pressure variations in a fluid are typically caused by gravity (since P = P0 + ρgh), but in general buoyant forces act opposite the direction of the frame of reference acceleration.
          • Under conditions of apparent weightlessness there can be no buoyant forces.
      • Archimedes' Principle
        • The magnitude of the buoyant force on an object is equal to the weight of the fluid it displaces.
         
        B = Wfluid displaced = ρfluidVdisplacedg
         
        • The factors that affect buoyancy are …
          • the density of the fluid,
          • the volume of the fluid displaced, and
          • the local acceleration due to gravity.
        • The buoyant force is not affected by …
          • the mass of the immersed object or
          • the density of the immersed object.
      • Objects immersed in a fluid have an apparent weight that is …
        • reduced by the buoyant force,
        		W′ = W − B
        • less than their actual weight,
        		W′ < W
        • directly proportional to the
          relative density (ρ′ = ρobject − ρfluid)
        		W′ = ρ′gV
      Buoyancy and Density
       densities  B > Wobject  B = Wobject  B < Wobject 
      ρobject < ρfluid object rises
      (wholly immersed )      		 float on surface
      (partly immersed)      		  
      ρobject = ρfluid   neutral buoyancy
      (wholly immersed)      		  
      ρobject > ρfluid     object sinks
       
    4. Fluid Flow
      • Continuity Equation - conservation of mass for fluids (mass per volume = mass density)
         
        Δm  =  ρΔV  =  ρAΔs  = ρAv = constant
        Δt Δt Δt
         
      • Bernoulli's Equation - conservation of energy for fluids (energy per volume = energy density)
         
        P1 + ½ ρv12 + ρgh1 = P2 + ½ ρv22 + ρgh2 
         
    5. Viscosity
      • Viscosity (also known as dynamic viscosity, absolute viscosity, or simple viscosity) is …
        • represented by the Greek letter η (eta).
        • defined informally as the quantity that describes a fluid's resistance to flow.
        • defined mathematically as the ratio of the shearing stress to the velocity gradient in a fluid.

          η =  ⎛
          ⎜
          ⎝          		 F ⎞
          ⎟
          ⎠          		  ÷  ⎛
          ⎜
          ⎝          		 Δvx ⎞
          ⎟
          ⎠          		 or η =  ⎛
          ⎜
          ⎝          		 F ⎞
          ⎟
          ⎠          		  ÷  ⎛
          ⎜
          ⎝          		 dvx ⎞
          ⎟
          ⎠
          A Δz A dz

        • often expressed using Newton's equation for fluids (which is similar to Newton's second law of motion).
                           
          F  =  η  Δvx or F  =  η  dvx
          A Δz A dz
                           
        • Units
          • The SI unit of viscosity is the pascal second [Pa·s].
          • The Gaussian unit of viscosity is the poise [P = dyne·s/cm2].
          • Ten poise equal one pascal second [10 P = 1 Pa·s].
      • Kinematic viscosity is …
        • represented by the Greek letter ν (nu).
        • defined informally as a measure of the resistive flow of a fluid under the influence of gravity.
        • defined mathematically as the ratio of the viscosity of a fluid to its density.
             
          ν =  η
          ρ
             
        • Units
          • The SI unit of kinematic viscosity is the square meter per second [m2/s].
          • The Gaussian unit of kinematic viscosity is the stokes [St = cm2/s].
          • Ten thousand stokes equal one square meter per second [10,000 stoke = 1 m2/s].
      • Factors Affecting Viscosity
        • Viscosity varies with material. (Viscosity is a property of materials.)
        • The viscosity of simple liquids …
          • decreases with increasing temperature
          • increases under very high pressures.
        • The viscosity of gases …
          • increases with increasing temperature
          • is independent of pressure and density.
    6. Aerodynamic Drag
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    7. Flow Regimes
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