thermal physics topic 10.1 ideal gases. boyle’s law w states that the pressure of a fixed mass of...
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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