Kinetic theory and phase change
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Kinetic Theory and Phase Change. Kinetic Theory Comparison with Ideal Gas RMS velocity examples PVT Diagrams Phase Changes Vapor Pressure and Humidity Examples. Ideal Gas Animation. Gas/piston animation (Java animation) (Flash animation) Note

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Kinetic Theory and Phase Change

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Kinetic theory and phase change

Kinetic Theory and Phase Change

  • Kinetic Theory

  • Comparison with Ideal Gas

  • RMS velocity examples

  • PVT Diagrams

  • Phase Changes

  • Vapor Pressure and Humidity

  • Examples


Ideal gas animation

Ideal Gas Animation

  • Gas/piston animation

    (Java animation)

    (Flash animation)

  • Note

    • Molecule collides with wall, gives it a little Impulse. (F Δt)

    • No more impulse until it makes round trip, then hits again. (box size)

    • N molecules with average velocity

    • Molecules moving equally in x, y, z directions


Kinetic theory

Kinetic Theory

  • A little Physics 103

    • Change in x-momentum for molecule hitting wall:

    • Time for molecule to travel 2l and hit again:

    • Average force during this time:

    • Average force of N molecules:

    • Average x-velocity-squared = 1/3 average total-velocity-squared

    • Pressure is thus:

      V is volume


Kinetic theory results 1

Kinetic Theory Results - 1

  • Previous page

  • Multiply by volume and rearrange like kinetic energy

  • Result

    • P inversely proportional to V

    • PV proportional to N

    • PV proportional to


Ideal gas law molecules version

Ideal Gas Law - #molecules version

  • Ideal Gas Law

    PV = nRT

  • Using #molecules:

    PV = NkT

    • N = nNA (N number of molecules)

    • k= R/NA (NA Avagadro’s number)

    • P in Pascals (no alternative units)

    • V in m3

    • T in K°

  • Boltzman’s constant

    • k = R/NA = 1.38e-12 J/K


Kinetic theory results 2

Kinetic Theory Results - 2

  • Comparing Kinetic Theory

  • With Ideal Gas Law

  • Gives

  • 4. Average Kinetic Energy


Kinetic theory examples

Kinetic Theory Examples

  • Root-mean-square velocity

  • Example 13-16 - Average translational KE at 37°C

  • Example 13-17 - rmsspeed of O2 and N2 at 20°C

    Mass N2

    RMS velocity N2


Pv diagrams

PV diagrams

  • Pressure vs. Volume at constant Temperature

    • Plot pressure vs. volume curves at constant temperature.

    • Different PV curves for different temperatures. (T “parameter”)

    • Different PV curves for different # moles. (usually constant)

    • Can plot in 3-D PVT diagram with 3rd temperature axis.


Pv diagrams with phase change

PV diagrams with phase change*

  • Pressure vs. Volume at constant Temperature.

    • At high temperatures PV varies normally (ideal gas).

    • As temperature is lowered PV becomes distorted.

    • As temperature is lowered further, liquid forms (critical point).

    • As temperature is lowered below critical point, liquid-vapor phase coexist

      *Non-ideal gas


3 d pvt diagrams with phase change

3-D PVT Diagrams with Phase Change

  • Trace PV line at constant temperature (red)

  • Trace PT line at constant pressure (blue)


3 d pvt diagram projections

3-D PVT diagram projections

  • PV diagram is projection to the right

  • PT diagram is projection to the left


Pt diagrams phase diagrams

PT diagrams (Phase diagrams)

  • Pressure vs. Temperature at constant Pressure.

    • Below 0.006 atm water sublimes directly from solid to vapor with increasing temperature. (vapors love vacuums!)

    • At 0.006 atm, solid/liquid/vapor water coexists at 0.01°C (triple point).

    • From 0.006 to 1.0 atm, water melts above 0°C, boils below 100 °C. (Rocky Mountain pressure cooker!)

    • At 1.0 atm water melts at 0°C, boils at 100°C (for us folks at sea level).

    • From 1.0 to 218 atm, water boils between 100°C to 374°C.

    • Above 374°C water doesn’t exist as liquid at any pressure (critical point).

Gases - Low Pressures, high temperatures

Solids - High pressures, low temperatures Liquids - In between


Vapor pressure

Vapor pressure

  • Partial pressure of water vapor in equilibrium with liquid water.

  • Saturated Vapor Pressure (maximum PP) varies with temperature.

  • Relative Humidity


Problem 67

Problem 67

  • What is the partial pressure of water on a day when the temperature is 25°C and the relative humidity is 40% ?

  • SVP from table

  • Relative Humidity


Problem 69

Problem 69

  • If the humidity in a room of volume 680 m3 at 25°C is 80%, what mass of water can still evaporate from an open pan?

  • SVP from table

  • Using Ideal Gas for partial pressures

  • 80% of 865 moles evaporated, 20% left

  • Mass of 173 moles water


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