• An?ideal gas?is one which 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

Boyle’s Law

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

• This leads to the relationship between the pressure and volume for a fixed mass of gas at constant temperature:

P₁V₁?= P₂V₂

Charles's Law

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

V ∝ T

• This leads to the relationship between the volume and thermodynamic temperature for a fixed mass of gas at constant pressure:

Pressure Law

• If the volume V is constant, the the?Pressure law?is given by:

P ∝ T

• This leads to the relationship between the pressure and thermodynamic temperature for a fixed mass of gas at constant volume:

Step 1: State the known values

• • Volume,?V?= 4.5 × 10^?3?m³
  • Initial pressure, P₁?= 6.2 × 10⁵?Pa
  • Initial temperature, T₁?= 30°C = 303 K
  • Initial temperature, T₂?= 40°C = 313 K

Step 2: Since volume is constant, state the pressure law