Cliste School
Get started

Heat & Thermodynamics

Gas Laws

5th Year · 6th Year (Leaving Cert)

  • ✓By the end of this lesson students will be able to state and apply Boyle's Law.
  • ✓By the end of this lesson students will be able to state and apply Charles's Law, understanding the importance of absolute temperature.
  • ✓By the end of this lesson students will be able to state and apply the Pressure Law, understanding the importance of absolute temperature.
  • ✓By the end of this lesson students will be able to state and apply the Ideal Gas Equation (Higher Level), defining all terms and units.
  • ✓By the end of this lesson students will be able to convert temperatures between Celsius and Kelvin scales.

Key concepts

Boyle's Law

Boyle's Law states that for a fixed mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. This means that if the pressure increases, the volume decreases proportionally, and vice versa.

pV = constant (or p₁V₁ = p₂V₂)
Charles's Law

Charles's Law states that for a fixed mass of gas at constant pressure, the volume of the gas is directly proportional to its absolute temperature. It is crucial that temperature is expressed in Kelvin (absolute temperature) for this law to hold true.

V/T = constant (or V₁/T₁ = V₂/T₂)
Pressure Law (Gay-Lussac's Law)

The Pressure Law states that for a fixed mass of gas at constant volume, the pressure of the gas is directly proportional to its absolute temperature. As with Charles's Law, temperature must be expressed in Kelvin.

p/T = constant (or p₁/T₁ = p₂/T₂)
Absolute Zero and Kelvin Scale

Absolute zero is the theoretical lowest possible temperature, at which particles have minimum kinetic energy. It is defined as 0 Kelvin (0 K) or approximately -273.15 °C. The Kelvin scale is an absolute temperature scale, where 0 K is absolute zero. To convert from Celsius to Kelvin, add 273.15: T(K) = T(°C) + 273.15.

T(K) = T(°C) + 273.15
Ideal Gas (HL)

An ideal gas is a theoretical gas composed of many randomly moving point particles that do not interact with each other except through elastic collisions. Key assumptions for an ideal gas are: the particles have negligible volume, there are no intermolecular forces between particles, and collisions are perfectly elastic. Real gases approximate ideal gas behaviour at high temperatures and low pressures.

Ideal Gas Equation (HL)

The Ideal Gas Equation combines Boyle's Law, Charles's Law, and the Pressure Law into a single relationship that describes the behaviour of an ideal gas. It relates the pressure (p), volume (V), number of moles (n), absolute temperature (T), and the universal gas constant (R).

pV = nRT

Key facts to remember

  • 1Boyle's Law: pV = constant (for fixed mass, constant T)
  • 2Charles's Law: V/T = constant (for fixed mass, constant p)
  • 3Pressure Law: p/T = constant (for fixed mass, constant V)
  • 4Always use absolute temperature (Kelvin) for Charles's Law, Pressure Law, and the Ideal Gas Equation.
  • 5To convert Celsius to Kelvin: T(K) = T(°C) + 273.15.
  • 6Absolute zero is 0 K or -273.15 °C.
  • 7The Ideal Gas Equation (HL) is pV = nRT, where p is pressure (Pa), V is volume (m³), n is moles (mol), R is the universal gas constant (8.31 J K⁻¹ mol⁻¹), and T is absolute temperature (K).
  • 8An ideal gas has negligible particle volume and no intermolecular forces.

Worked examples

Example 1

A gas occupies a volume of 3.0 L at a pressure of 120 kPa. If the temperature remains constant, what will be the new volume if the pressure is increased to 180 kPa?

IIdentify known values: p₁ = 120 kPa, V₁ = 3.0 L, p₂ = 180 kPa.
IIIdentify unknown value: V₂.
IIISince temperature is constant, apply Boyle's Law: p₁V₁ = p₂V₂.
IVSubstitute the known values into the formula: (120 kPa)(3.0 L) = (180 kPa)V₂.
VRearrange the equation to solve for V₂: V₂ = (120 kPa * 3.0 L) / 180 kPa.
VICalculate the result: V₂ = 360 / 180 = 2.0 L.

Answer

2.0 L

Units for pressure and volume can be kept consistent (e.g., kPa and L) as long as they are on both sides of the equation.

Example 2

A balloon contains 4.5 L of air at 20 °C. If the pressure remains constant, what will be the volume of the balloon if the temperature is increased to 80 °C?

IIdentify known values: V₁ = 4.5 L, T₁ = 20 °C, T₂ = 80 °C.
IIIdentify unknown value: V₂.
IIIConvert temperatures from Celsius to Kelvin: T₁(K) = 20 + 273.15 = 293.15 K, T₂(K) = 80 + 273.15 = 353.15 K.
IVSince pressure is constant, apply Charles's Law: V₁/T₁ = V₂/T₂.
VSubstitute the known values into the formula: 4.5 L / 293.15 K = V₂ / 353.15 K.
VIRearrange the equation to solve for V₂: V₂ = (4.5 L * 353.15 K) / 293.15 K.
VIICalculate the result: V₂ = 5.42 L (to 3 significant figures).

Answer

5.42 L

Always convert temperatures to Kelvin when using Charles's Law or the Pressure Law.

Example 3

(HL) Calculate the volume occupied by 0.50 moles of an ideal gas at a pressure of 1.01 x 10⁵ Pa and a temperature of 30 °C. (Universal gas constant R = 8.31 J K⁻¹ mol⁻¹)

IIdentify known values: n = 0.50 mol, p = 1.01 x 10⁵ Pa, T = 30 °C, R = 8.31 J K⁻¹ mol⁻¹.
IIIdentify unknown value: V.
IIIConvert temperature from Celsius to Kelvin: T(K) = 30 + 273.15 = 303.15 K.
IVApply the Ideal Gas Equation: pV = nRT.
VRearrange the equation to solve for V: V = nRT / p.
VISubstitute the known values (ensuring SI units): V = (0.50 mol * 8.31 J K⁻¹ mol⁻¹ * 303.15 K) / (1.01 x 10⁵ Pa).
VIICalculate the result: V = (1259.4645) / (101000) = 0.01247 m³.
VIIIRound to an appropriate number of significant figures: V = 0.0125 m³.

Answer

0.0125 m³

Ensure all quantities are in SI units (Pascals for pressure, cubic metres for volume, Kelvin for temperature) when using the Ideal Gas Equation with R.

Common mistakes

  • ✗Failing to convert temperature from Celsius to Kelvin before applying Charles's Law, Pressure Law, or the Ideal Gas Equation.
  • ✗Using inconsistent units for pressure or volume in calculations, especially with the Ideal Gas Equation (e.g., using L for V instead of m³).
  • ✗Confusing which variable is held constant for each of the individual gas laws.
  • ✗Incorrectly recalling the value or units of the universal gas constant, R (HL).
  • ✗Not identifying that the mass of gas must be fixed for Boyle's, Charles's, and Pressure Laws to apply.

Exam tips

  • ★Read the question carefully to identify which variables are constant and which law is applicable.
  • ★Always write down the relevant formula first, then list your knowns and unknowns.
  • ★Show all steps in your calculations, including any unit conversions, to maximise marks.
  • ★Pay close attention to units. Ensure all quantities are in SI units (Pa, m³, K) when using the Ideal Gas Equation.
  • ★For Higher Level, remember the value and units of the universal gas constant, R (8.31 J K⁻¹ mol⁻¹).

Ready to practise?

Try a problem on this topic

Snap a photo or type a question — get step-by-step working instantly.

Solve a problem →← Physics curriculum