THERMO2 Flashcards Preview

Thermodynamics > THERMO2 > Flashcards

Flashcards in THERMO2 Deck (33):
1

Ideal Gas Equation

PV = nRT

P = pressure
V = volume
n = number of moles
R = molar gas constant
T = temperature

2

Assumptions of Kinetic Gas Theory

1. Gas contains many molecules
2. Molecules are well separated
3. Direction of motion of molecules is random
4. Molecules exert no force on each other except during collisions
5. Collisions between molecules and with walls are elastic

3

Ideal Gas Constant

R = PV/nT = 8.31

4

When do real gases behave as ideal gases?

Real gases behave as ideal gases when molecules are well separated i.e. at high temperatures and low pressures

5

Units of Pressure
1 pascal

1Pa = 1 N/m^2

6

Units of Pressure
1 bar

1 bar = 10^5 Pa

7

Units of Pressure
1 atmosphere

1 atm = 1013millibar = 1.013x10^5 Pa

8

Standard Temperature and Pressure (STP)

0C = 273.15K
1atm = 1.013x10^5 Pa

9

How does kinetic gas theory explain pressure?

Collisions of molecules with the walls of the container
Change in momentum

10

Pressure Equation

P = (1/3) * Nm/V * (v^2)av

11

Kinetic Energy per Molecule

(1/2)mv^2 = (3/2)kT

12

Dalton's Law of Partial Pressures

Ptotal = P1 + P2
Pt =RT/V (n1 + n2)

13

Pressure in a Fluid

P = ρhg

14

Kinetic Energy per Mole

(1/2)Mv^2 = (3/2)RT

15

Number of Molecules and Moles Equation

N = n*Na

N = number of molecules
n = number of Moles
Na = advogadros constant

16

Mass of Molecules and Moles Equation

M = m*Na

M = mass of a mole
m =mass of a molecule
Na = advogadros Constant

17

Relationship between advogadros Constant, the molar Gas Constant and Boltzmann Constant

R = k*Na

18

Root Mean Square Speed Equation

Vrms = √(Vav^2) = √(3kT/m)

19

Mean Free Path
Definition

The average distance travelled by a Molecule between collisions

20

Mean Free Path
Equation

λ = 1/(√2*nv*π*d²)

λ = mean free path
nv = number density
d = diameter of a molecule

21

What does mean free path depend on?

-size of molecules
-particle density of the gas
-doesn't depend on speed
-depends on geometric factors

22

Collision Time
Definition

The average time between collisions

23

Collision Time
Equation

λ = Vav * τ

τ = collision Time
λ = mean free path
Vav = average velocity

24

What does collision time depend on?

-mean free path
-speed of molecules

25

NND

Nearest Neighbour Distance

NND = ∛(volume per molecule)
NND = ∛(1/nv) = ∛(V/N) = ∛(kT/P)

26

Maxwell Boltzmann Distribution
Description of Graph

-bell curve
-steeper on left hand side
-doesn't touch the y axis
-theoretically the Graph continues to x=∞
-speed on X axis
-fraction of molecules on y axis

27

Maxwell Boltzmann Distribution
Vmax

Vmax is the speed that the highest proportion of molecules have
I.e. The maxima of the Graph
To find it differentiate the Graph equation and set it equal to zero
Vmax = √(2RT/M)

28

Maxwell Boltzmann Distribution
Vrms

The square root of the average of the speeds squared
Calculated using an integral
Vrms = √(3kT/m) = √(3RT/M)

29

Maxwell Boltzmann Distribution
Vav

Average of the velocities of each molecule so accounts for direction
Calculated using an integral
Vav = √(8kT/πm) = √(8RT/πM)

30

Relationship Between Vmax, Vrms and Vav

Vmax < Vav < Vrms

31

Maxwell Boltzmann Distribution
Change With Temperature

For a fixed mass of gas, an increase in temperature results in:
-Vmax increases
-peak moves to the right
-height decreases
-area under graph remains constant as the number of molecules has not changed

32

Maxwell Boltzmann Distribution
Change With Molar Mass

Temperature remains constant but molar mass is increased results in:
-Vmax decreased
-height of graph increases
-area under graph remains constant as the number of molecules has not changed

33

Maxwell Boltzmann Distribution
Evaporative Cooling - Change With Loss of Fast Molecules

-the fastest molecules are lost
-once thermal equilibrium is achieved again after the initial loss, the graph:
-Vmax decreased
-height decreased and area under the graph has decreased as there are fewer molecules than their were before the evaporative Cooling