IB Physics SL

Revision Notes

3.2.1 Ideal Gas Laws

Ideal Gas Laws

Boyle’s Law

  • Boyle’s Law states:

For a fixed mass of gas at a constant temperature, the pressure p is inversely proportional to the volume V

  • This can be expressed in equation form as:

  • Plotting the pressure against the volume for a gas at a constant temperature on a graph (i.e. pV graph) gives the so-called isothermal curve for the gas

 

  • Plotting the pressure against the reciprocal of the volume (i.e. 1/V) for a gas at constant temperature still gives an isothermal, but this time, the line is straight

 

  • Boyle’s law can be rewritten as follows:

pV = constant

  • Which means that:

p1V1 = p2V2

  • Where:
    • p1 = initial pressure in pascals (Pa) or atmospheres (atm)
    • V1 = initial volume in metres cubed (m3) or litres (L)
    • p2 = the final pressure in pascals (Pa) or atmospheres (atm)
    • V2 = the final volume in metres cubed (m3) or litres (L)

Charles’s Law

  • Charle’s Law states:

For a fixed mass of gas at constant pressure, the volume V is directly proportional to the absolute temperature T

  • This can be expressed in equation form as:

  • The direct proportionality relationship is only valid if the gas temperature is measured in kelvin (K)
  • Plotting the volume against the temperature for a gas at constant pressure gives a straight line along which the gas pressure does not change

 

  • Charles’s law can be rewritten as follows:

  • Which means that:

  • Where:
    • V1 = initial volume in metres cubed (m3) or litres (L)
    • T1 = initial temperature in kelvin (K)
    • V2 = final volume in metres cubed (m3) or litres (L)
    • T2 = final temperature in kelvin (K)

Gay Lussac’s Law

  • Gay Lussac’s Law states:

For a fixed mass of gas at constant volume, the pressure p is directly proportional to the absolute temperature T

  • This can be expressed in equation form as:

  • The direct proportionality relationship is only valid if the gas temperature is measured in kelvin (K)
  • Plotting the pressure against the temperature for a gas at constant volume gives a straight line along which the gas volume is the same

 

  • Gay Lussac’s law can be rewritten as follows:

  • Which means that:

  • Where:
    • p1 = initial pressure in pascals (Pa) or atmospheres (atm)
    • T1 = initial temperature in kelvin (K)
    • p2 = final pressure in pascals (Pa) or atmospheres (atm)
    • T2 = final temperature in kelvin (K)

Gas Laws Combined

  • The three gas laws can be combined into one
  • For a fixed mass of gas, the following holds:

  • Which means that:

  • Where:
    • p1 = initial pressure in pascals (Pa) or atmospheres (atm)
    • V1 = initial volume in metres cubed (m3) or litres (L)
    • T1 = initial temperature in kelvin (K)
    • p2 = final pressure in pascals (Pa) or atmospheres (atm)
    • V2 = final volume in metres cubed (m3) or litres (L)
    • T2 = final temperature in kelvin (K)

Worked Example

An ideal gas occupies a volume equal to 5.0 × 10–4 m3. Its pressure is 2.0 × 106 Pa and its temperature is 40°C. The gas is then heated and reaches a temperature of 80°C. It also expands to a new volume of 6.0 × 10–4 m3.

Determine the new pressure of the gas.

Step 1: Write down the given quantities

    • Initial volume, V1 = 5.0 × 10–4 m3
    • Initial pressure, p1 = 2.0 × 106 Pa
    • Initial temperature, T1 = 40°C = 313 K
    • Final volume, V2 = 6.0 × 10–4 m3
    • Final temperature, T2 = 80°C = 353 K

Remember to:

    • Use the appropriate subscripts for initial (i.e. 1) and final (i.e. 2) values
    • Convert the temperature from degrees Celsius into Kelvin (K)

Step 2: Write down the equation for the three gas laws combined

Step 3: Rearrange the equation to calculate the unknown final pressure p2

Step 4: Substitute numbers into the equation 

p2 = 1.9 × 106 Pa

Exam Tip

When dealing with gas laws problems, always remember to convert temperatures from degrees Celsius (°C) to kelvin (K).

After you solve a problem using any of the gas laws (or all of them combined), always check whether your final result makes physically sense – e.g. if you are asked to calculate the final pressure of a fixed mass of gas being heated at constant volume, your result must be greater than the initial pressure given in the problem (since Gay- Lussac’s law states that pressure and absolute temperature are directly proportional at constant volume).

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