• The ideal gas laws are the experimental relationships between?pressure?(P), volume (V) and temperature (T) of an ideal gas
• The mass and the number of molecules of the gas is assumed to be constant for all of these

Boyle’s Law

• If the temperature?T?of an ideal gas is constant, then?Boyle’s Law?is given by:

• This means the pressure is?inversely proportional?to the volume of a gas
• The relationship between the pressure and volume for a fixed mass of gas at constant temperature can also be written as:

P1V1?= P2V2

• Where:
  • P1?= initial pressure (Pa)
  • P2?= final pressure (Pa)
  • V1?= initial volume (m3)
  • V2?= final volume (m3)

   

Boyle's Law graph representing pressure inversely proportional to volume

• If the temperature increases, the graph is further from the origin and vice versa

Charles's Law

• If the pressure?P?of an ideal gas is constant, then?Charles’s law?is given by:

V ∝ T

• This means the volume is?proportional?to the temperature of a gas
• The relationship between the volume and thermodynamic temperature for a fixed mass of gas at constant pressure can also be written as:

• Where:
  • V1?= initial volume (m3)
  • V2?= final volume (m3)
  • T1?= initial temperature (K)
  • T2?= final temperature (K)

   

Charles's Law graph representing temperature (in °C) directly proportional to the volume

• The Charles's Law graph for temperature in?kelvin?against volume is identical except that is a straight line through the?origin

Pressure Law

• If the volume?V?of an ideal gas is constant, the?Pressure law?is given by:

P?∝?T

• This means the pressure is?proportional?to the temperature
• The relationship between the pressure and thermodynamic temperature for a fixed mass of gas at constant volume can also be written as:

• Where:
  • P1?= initial pressure (Pa)
  • P2?= final pressure (Pa)
  • T1?= initial temperature (K)
  • T2?= final temperature (K)

   

Pressure Law graph representing temperature (in °C) directly proportional to the volume

• An?ideal gas?is one that obeys the relation:

pV?∝?T

• Where:
  • p?=?pressure?of the gas (Pa)
  • V?= volume of the gas (m3)
  • T?=?thermodynamic temperature?(K)

   

• The molecules in a gas move around randomly at high speeds, colliding with surfaces and exerting pressure upon them

Gas molecules move about randomly at high speeds

• Imagine molecules of gas free to move around in a box
• The temperature of a gas is related to the average speed of the molecules:
  • The hotter the gas, the faster the molecules move
  • Hence the molecules collide with the surface of the walls more frequently

   

• Since force is the rate of change of?momentum:
  • Each collision applies a?force?across the surface area of the walls
  • The faster the molecules hit the walls, the greater the force on them

   

• Since pressure is the?force per unit area
  • Higher temperature leads to higher pressure

   

• If the volume?V?of the box decreases, and the temperature?T?stays constant:
  • There will be a smaller surface area of the walls and hence more collisions
  • This also creates more pressure

   

• Since this equates to a greater force per unit area,?pressure?in an ideal gas is therefore defined by:

The frequency of collisions of the gas molecules per unit area of a container

Molecular model of the three ideal gas laws

Step 1: Ideal gas relation between pressure, volume and temperature

pV?∝?T

Step 2: Write the equation in full

pV?=?kT

• • Where?k = the constant of proportionality

Step 3:?Rearrange for the constant of proportionality

Step 4: Convert temperature T into Kelvin

θ °C + 273.15 = T K

30 °C + 273.15 = 303.15 K

Step 5:?Substitute in known value into constant of proportionality equation

Step 6: Rearrange ideal gas relation equation for pressure

Step 7: Substitute in new values

k?= 9.203...

V?stays the same = 4.5 × 10-3?m3

T?= 40 °C?= 40 + 273.15 = 313.15 K