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 oil Bourdon Pressure gauge Volume of dry air Air from foot pump 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 Experiment Tap 1 Fixed mass of gas Mercury in U tube Tap 2 Tap 3 Water reservoir Fixed mass of 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 oC A value for absolute zero V T K

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 Water Fixed Mass of gas Heat

What to do Change the temperature of the water by heating it Record the pressure of the gas

The Results P T oC A value for absolute zero P T K

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