Thermal PhysicsTopic 3.2 Modelling Gases

Courtesy to Greengates school in mexico 

Understandings: Pressure Equation of state for an ideal gas Kinetic model of an ideal gas Mole, molar mass and the Avogadro constant Differences between real and ideal gases

Applications and skills: Solving problems using the equation of state for an ideal

gas and gas laws Sketching and interpreting changes of state of an ideal

gas on pressure–volume, pressure–temperature and volume–temperature diagrams

The Mole

The mole is the amount of substance which contains the same number of elementary entities as there are in 12 grams of carbon-12

Experiments show that this is 6.02 x 1023 particles A value denoted by NA and called the

Avogadro Constant (units mol-1)

Molar Mass

Molar mass is the mass of one mole of the substance

SI units are kg mol-1

Example

Molar mass of Oxygen gas is

32 x10-3 kg mol-1

If I have 20g of Oxygen, how many moles do I have and how many molecules?

20 x 10-3 kg / 32 x10-3 kg mol-1

0.625 mol 0.625 mol x 6.02 x 1023 molecules 3.7625 x 1023 molecules

Thermal Properties of Gases

Investigations involved the measurement of • Pressure• Volume• Temperature

These experiments used these macroscopic properties of a gas to formulate a number of gas laws

Units

Temperature is always measured in K Volume is usually in m3

Pressure can be different units as long as you are consistent

But 1 atm = 1.01 x 105 Nm-2

= 101.3 kPa = 760 mmHg

Pressure

Pressure can be explained by the collisions with the sides of the container

If the temperature increases, the average KE of the particles increases

The increase in velocity of the particles leads to a greater rate of collisions and hence the pressure of the gas increases as the collisions with the side have increased

Also the change in momentum is greater, therefore greater force

Pressure continued

When a force is applied to a piston in a cylinder containing a volume of gas

The particles take up a smaller volume Smaller area to collide with And hence collisions are more frequent

with the sides leading to an increase in pressure

Also, as the piston is being moved in It gives the particles colliding with it more

velocity Therefore they have more KE Therefore the temperature of the gas rises.

Collisions

Because the collisions are perfectly elastic

There is no loss of KE as a result of the collisions

An Ideal Gas

Is a theoretical gas that obeys the gas laws

And thus fit the ideal gas equation exactly

Real Gases

Real gases conform to the gas laws under certain limited conditions

But they condense to liquids and then solidify if the temperature is lowered

Furthermore, there are relatively small forces of attraction between particles of a real gas

This is not the case for an ideal gas

The Kinetic Theory of Gases

When the moving particle theory is applied to gases it is generally called the kinetic theory

The kinetic theory relates the macroscopic behaviour of an ideal gas to the microscopic behaviour of its molecules or atoms

The Postulates

Gases consist of tiny particles called atoms or molecules

The total number of particles in a sample is very large

The particles are in constant random motion The range of the intermolecular forces is

small compared to the average separation

The Postulates continued

The size of the particles is relatively small compared with the distance between them

Collisions of a short duration occur between particles and the walls of the container

Collisions are perfectly elastic

The Postulates continued

No forces act between the particles except when they collide

Between collisions the particles move in straight lines

And obey Newton’s Laws of motion

Macroscopic Behaviour

The large number of particles ensures that the number of particles moving in all directions is constant at any time

Boyle’s Law

States that the pressure of a fixed mass of gas is inversely proportional to its volume at constant temperature (isothermal transformation)

P 1/V or PV = constant When the conditions are changed P1V1 = P2V2

The Experiment

Boyle’s law You-tubes

Marshmallow in vacuum• http://www.youtube.com/watch?feature=endscre

en&v=OHY9fFQhX68&NR=1

Shaving cream in vacuum• http://www.youtube.com/watch?v=RPlCO3AIT

V4&feature=related

Balloon in vacuum• http://www.youtube.com/watch?v=J_I8Y-i4Axc

The Results

P

V

P

1/ V

Charles’ Law

States that the volume of a fixed mass of gas is directly proportional to its absolute temperature at constant pressure

V T or V/T = constant

When the conditions are changed V1/T1 = V2/T2

The Experiment

The Results

V

T K

V

T oCA value forabsolute zero

The Pressure Law

States that the pressure of a fixed mass of gas is directly proportional to its absolute temperature at constant volume

P T or P/T = constant

When the conditions are changed P1/T1 = P2/T2

The Experiment

The Pepsi can• http://www.youtube.com/watch?v=PeHIN-HM

wM4

The Results

P

T K

P

T oCA value forabsolute zero

Apply your knowledge!

Absolute Zero and the Kelvin Scale Charles’ Law and the Pressure Law suggest that there

is a lowest possible temperature that substances can go• This is called Absolute Zero

The Kelvin scale starts at this point and increases at the same scale as the Celsius Scale• Therefore -273oC is equivalent to 0 K• ∆1oC is the same as ∆1 K• To change oC to K, add 273• To change K to oC, subtract 273

Combining the Laws

The gas laws can be combined to give a single equation

For a fixed mass of gas its pressure times its volume divided by its absolute temperature is a constant

PV/T = k So that P1V1/T1 = P2V2/T2

Ideal Gas equation: PV = nRT Where n is the number of moles R is the universal gas constant 8.31 J mol-1 K-1

Be a Thinker!

Be a Thinker!

Ideal Gas versus real gas

An ideal gas is a theoretical gas that obeys the gas laws• and thus fit the ideal gas equation exactly

Real gases conform to the gas laws at low pressures and large volumes.

they condense to liquids and then solidify if the temperature is lowered

there are relatively small forces of attraction between particles of a real gas• This is not the case for an ideal gas

Apply your knowledge!

Applying the ideal gas equation

Be a thinker!

Be a thinker!

Be a thinker!

Be a thinker!