Thermal Physics

Topic 10.1 Ideal Gases

Boyle’s Law

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

P 1/V or PV = constant

When the conditions are changed P1V1 = P2V2

The Experiment

Air fromfoot pump

Bourdon Pressuregauge

Volume of dry air

oil

What to do

A column of trapped dry air in a sealed tube by the oil

The pressure on this volume of air can be varied by pumping air in or out of the oil reservoir to obtain different pressures

Wait to allow the temperature to return to room temperature

The Results

P

V

P

1/ V

PV

P

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 ExperimentTap 1

Tap 2 Tap 3

Water reservoir

Fixed massof gas

Mercury in U tube

What to do

Fill the mercury column with mercury using the right hand tube (tap 1 open, tap 2 closed)

With tap 1 open drain some mercury using tap 2, then close tap 1 and 2. To trap a fixed mass of gas

Fill the jacket with water (make sure tap 3 is closed)

and then

Change the temperature of the water by draining some water from tap 3 and adding hot water

Equalise the pressure by leveling the columns using tap 2

Read the volume from the scale

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

Bourdon gauge

Ice

WaterFixedMass ofgas

Heat

What to do

Change the temperature of the water by heating it

Record the pressure of the gas

The Results

P

T K

P

T oCA value forabsolute zero

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

The 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

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

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