gas behavior formulas from models § 17.1–17.2. ideal gas model molecules: non-interacting point...

Gas Behavior

formulas from models

§ 17.1–17.2

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)

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

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

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

Ideal Gas EOS

• What is the pressure?

Lx

Ly

Lz

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

RMS Speed

1/2 mv2 = 3/2 kT

v2 = 3kT/m

M = molar mass

3kT/mv = 3RT/M=

Ideal Gas Model

Does not address interaction behavior

• condensation

• mean-free path

• sound transmission

• slow diffusion

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.

p-V plots

Ideal gas

Source: Y&F, Figure 18.6

Real Substance

Source: Y&F, Figure 18.7

Boyle’s Law

• Ideal gas at constant pressure

P1V1 = P2V2

• Pressure and volume inversely related

V-T plots

Gas

Source: Y&F, Figure 17.5b

P1

V

P2

P3

Charles’s Law

• Ideal gas at constant pressure

V2/T2 = V1/T1

• Volume and temperature directly related

p-T plots

Gas

Source: Y&F, Figure 17.5b

Elastic Moduli

reversible deformation

§ 17.3

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

Shear Modulus

• Deformation under shear stress

L0

• S = Shear Modulus

• Area parallel to force

= SFA

xL0

x

Bulk Modulus

• Volume change

• B = Bulk Modulus; Units: Pa

P = BVV0

V0 + V

V0

Phases of Matter

Behavior and diagrams

§ 17.4

Liquids

• Atoms constantly moving

• Molecules stay close to each other– do not separate– do not pass through each other– slide around

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?

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.)

Solid Water (Ice)

Source: M. Chaplin, Water Structure and Behavior. www.lsbu.ac.uk/water/ice1h.html

Solids

• Strong connections between atoms– rigidity and elasticity

• Atoms vibrate about fixed positions

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!

Variables and Diagrams

• State Variables: p, V, n, T

• Hard to visualize in 2-D

• Useful plots: p-V, p-T

p-V-T SurfaceIdeal Gas

Source: Y&F, Figure 18.27

p-V-T SurfaceReal Substance

Source: Y&F, Figure 18.26

p-T plotPhase Diagram

Source: Y&F, Figure 18.24

Water’s Phase Diagram

Source: P.W. Atkins, Physical Chemistry, 2 ed., 1978, p.193.

The Book is Wrong

About

•Salting cooking water– It doesn’t raise boiling temperature much

•Pressure melting of ice– not at attainable pressures