IB DP Physics: HL复习笔记3.2.1 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. p-V graph) gives the so-called isothermal curve for the gas

Graph of pressure against volume for a fixed mass of gas at three different temperatures, with T1 < T2 < T3. The curves are called isotherms (i.e. the temperature along each curve is constant)

• 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

Graph of pressure against reciprocal of the volume for a fixed mass of gas at three different temperatures, with T1 < T2 < T3. In this case, the isotherms are straight lines

• 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

Graph of volume against temperature for a fixed mass of gas at three different pressures, with p1 < p2 < p3

• 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

Graph of pressure against temperature for a fixed mass of gas at three different volumes, with V1 < V2 < V3

• 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)

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