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Kinetic Theory and Phase ChangePowerPoint Presentation

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
- 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

- 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

- 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
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

- Comparing Kinetic Theory
- With Ideal Gas Law
- Gives
- 4. Average Kinetic Energy

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

- 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*

- 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

- Trace PV line at constant temperature (red)
- Trace PT line at constant pressure (blue)

3-D PVT diagram projections

- PV diagram is projection to the right
- PT diagram is projection to the left

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

- Partial pressure of water vapor in equilibrium with liquid water.
- Saturated Vapor Pressure (maximum PP) varies with temperature.
- Relative Humidity

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

- 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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