# Kinetic Theory and Phase Change - PowerPoint PPT Presentation

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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

• 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