Describe the effects of temperature and pressure on the volume of a gas

States of Matter – Solids, Liquids & Gases

In this lesson we’ll focus on gases and how their volume changes when we play with temperature and pressure. Think of a gas like a crowd of people in a room – the more people (molecules) or the bigger the room (temperature), the more space they need.

Temperature and Volume – Charles’s Law

When you heat a gas, its molecules move faster and want more space. This is described by Charles’s Law:

$V \propto T$

or in equation form:

$V = kT$

🔍 Analogy: Imagine blowing up a balloon. The hotter the air inside, the bigger the balloon gets.

• Keep the pressure constant.
• Increase temperature → increase volume.
• Decrease temperature → decrease volume.

Pressure and Volume – Boyle’s Law

If you squeeze a gas, its molecules are forced closer together, reducing the space they occupy. Boyle’s Law states:

$P \propto \dfrac{1}{V}$

or:

$PV = \text{constant}$

💨 Analogy: Think of a spring-loaded air pump. Squeezing it (increasing pressure) makes the air inside compress (decrease volume).

1. Keep the temperature constant.
2. Increase pressure → decrease volume.
3. Decrease pressure → increase volume.

Combined Gas Law

When both temperature and pressure change, we combine the two laws:

$$\dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2}$$

📊 Example: A sealed balloon at 20 °C (293 K) and 1 atm has a volume of 2 L. If you heat it to 60 °C (333 K) while keeping pressure constant, the new volume is:

$V_2 = V_1 \dfrac{T_2}{T_1} = 2\,\text{L} \times \dfrac{333}{293} \approx 2.27\,\text{L}$

Pressure, Temperature & Volume – Ideal Gas Law

The most general equation for a gas is the Ideal Gas Law:

$$PV = nRT$$

Where:

• $P$ = pressure (Pa or atm)
• $V$ = volume (m³ or L)
• $n$ = number of moles
• $R$ = ideal gas constant (0.0821 L·atm K⁻¹ mol⁻¹)
• $T$ = temperature (K)

🔬 Tip: Always convert temperature to Kelvin before using the equation.

Exam Tips – Questions on Gas Laws

• Identify the variable that is held constant (pressure or temperature).
• Use the correct law: Charles for temperature, Boyle for pressure, or the Combined Law if both change.
• Remember to convert temperatures to Kelvin.
• Check units – they must match on both sides of the equation.
• For multiple-choice, look for the inverse relationship in Boyle’s Law and direct in Charles’s Law.

💡 Practice Question: A gas occupies 5 L at 1 atm and 300 K. If the pressure is increased to 2 atm while keeping temperature constant, what is the new volume?

$V_2 = \dfrac{P_1 V_1}{P_2} = \dfrac{1 \times 5}{2} = 2.5\,\text{L}$

Quick Reference Table