Gas Behavior

formulas from models

§ 18.3–18.4

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)

RMS Speed

1/2 mv2 = 3/2 kT

v2 = 3kT/m

M = molar mass

3kT/mv = 3RT/M=

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

Ideal Gas Model

Does not address interaction behavior

• condensation

• mean-free path

• sound transmission

• slow diffusion

van der Waals EOS

• Molecules have volume

• Molecules attract (dimerize)

p =an2

V 2

nRTV – nb

–

Heat Capacity

• Energy to raise the temperature of a sample of gas

Constant-Volume Heating

dU = dK + pdV

Ktr = 3/2 NkT

dKtr = 3/2 NkdT

dV= 0

Cv = dU/dT = 3/2 Nk = 3/2 nR

Heat capacity of an ideal gas

Constant-Volume Heating

dU = dK + pdV

Ktr = 3/2 NkT; Krot = 2/2 NkT

dKt = 5/2 NkdT

dV= 0

Cv = dU/dT = 5/2 Nk = 5/2 nR

Heat capacity of a diatomic gas

Heat Capacities of Solids

Six modes of motion

Kvib in x, y, z directions

Uel in x, y, z directions

U = 6N(1/2 kT) = 3NkT

dU = 3NkdT

dV 0

Cv = dU/dT = 3 Nk = 3 nR

Law of Dulong and Petit

Phases of Matter

Behavior and diagrams

§ 18.6

Variables and Diagrams

• State Variables: p, V, n, T

• Hard to visualize in 2-D

• Useful plots: p-V, p-T

p-V plots

Ideal gas

Source: Y&F, Figure 18.6

Real Substance

Source: Y&F, Figure 18.7

p-T plot

Gas

Source: Y&F, Figure 17.5b

p-T plotPhase Diagram

Source: Y&F, Figure 18.24

p-V-T SurfaceIdeal Gas

Source: Y&F, Figure 18.27

p-V-T SurfaceReal Substance

Source: Y&F, Figure 18.26