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Gas Behavior
formulas from models
§ 17.1–17.2
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Ideal Gas Model
• molecules: non-interacting point masses
• collide elastically with surfaces
Temperature T is related to kinetic energy K
• Ktr = 1/2 kT per mode of motion
• k = 1.3806505 10–23 J/K (Boltzmann constant)
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What determines the pressure of a sample of a gas? Increasing the volume:
A. Has no effect
B. Increases the pressure
C. Decreases the pressure
CPS Question
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What determines the pressure of a sample of a gas? Increasing the number of molecules:
A. Has no effect
B. Increases the pressure
C. Decreases the pressure
CPS Question
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What determines the pressure of a sample of a gas? Increasing the temperature:
A. Has no effect
B. Increases the pressure
C. Decreases the pressure
CPS Question
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Ideal Gas EOS
• What is the pressure?
Lx
Ly
Lz
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Ideal Gas Model
• shows expansion with increasing T at constant p
• shows p increase with increasing T at constant V
• shows p = 0 at T = 0 K
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RMS Speed
1/2 mv2 = 3/2 kT
v2 = 3kT/m
M = molar mass
3kT/mv = 3RT/M=
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Ideal Gas Model
Does not address interaction behavior
• condensation
• mean-free path
• sound transmission
• slow diffusion
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CPS Question
At constant temperature, how are pressure and volume of an ideal gas related?
A. They are directly proportional.
B. They are negatively correlated.
C. They are inversely proportional.
D. They are unrelated.
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p-V plots
Ideal gas
Source: Y&F, Figure 18.6
Real Substance
Source: Y&F, Figure 18.7
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Boyle’s Law
• Ideal gas at constant pressure
P1V1 = P2V2
• Pressure and volume inversely related
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V-T plots
Gas
Source: Y&F, Figure 17.5b
P1
V
P2
P3
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Charles’s Law
• Ideal gas at constant pressure
V2/T2 = V1/T1
• Volume and temperature directly related
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p-T plots
Gas
Source: Y&F, Figure 17.5b
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Elastic Moduli
reversible deformation
§ 17.3
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Young’s Modulus
• Fractional elongation under tensionor shortening under compression
L0
L0 + L
• Y = Young’s Modulus; Units: Pa
• Area perpendicular to force
= YFA
LL0
stress strain
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Shear Modulus
• Deformation under shear stress
L0
• S = Shear Modulus
• Area parallel to force
= SFA
xL0
x
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Bulk Modulus
• Volume change
• B = Bulk Modulus; Units: Pa
P = BVV0
V0 + V
V0
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Phases of Matter
Behavior and diagrams
§ 17.4
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Liquids
• Atoms constantly moving
• Molecules stay close to each other– do not separate– do not pass through each other– slide around
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Think Question
In liquids, molecules are close together. In gases, molecules are far apart. Are the molecules’ potential energies higher when they are together in the liquid or when they are separated in the gas?
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Think Question
If the molecules of a gas, without any outside force acting on them, move toward each other and condense to form a liquid, will their kinetic energies increase or decrease? (Hint: in an isolated system, total energy is conserved.)
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Solid Water (Ice)
Source: M. Chaplin, Water Structure and Behavior. www.lsbu.ac.uk/water/ice1h.html
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Solids
• Strong connections between atoms– rigidity and elasticity
• Atoms vibrate about fixed positions
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Phase Changes
• Potential energies:
Solid < Liquid < Gas
• During a phase change, potential energy, not kinetic energy (temperature) changes.
• Heating or cooling a changing phase does not change its temperature!
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Variables and Diagrams
• State Variables: p, V, n, T
• Hard to visualize in 2-D
• Useful plots: p-V, p-T
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p-V-T SurfaceIdeal Gas
Source: Y&F, Figure 18.27
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p-V-T SurfaceReal Substance
Source: Y&F, Figure 18.26
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p-T plotPhase Diagram
Source: Y&F, Figure 18.24
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Water’s Phase Diagram
Source: P.W. Atkins, Physical Chemistry, 2 ed., 1978, p.193.
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The Book is Wrong
About
•Salting cooking water– It doesn’t raise boiling temperature much
•Pressure melting of ice– not at attainable pressures