1. What Is Expansion of Gases?
Gases expand much more than solids and liquids when heated. Their particles are already far apart, and when they gain more energy, they move even faster and spread out. This makes the gas occupy a larger volume.
Because of this large expansion, gases show noticeable changes in volume and pressure even with small temperature changes.
2. Why Gases Expand So Much
Particles in a gas move freely and have very weak intermolecular forces. When heat is supplied, they move even faster, pushing outward in all directions. This rapid motion makes gases expand strongly.
2.1. Large Increase in Particle Motion
Heating increases the speed of gas particles. Since they are not bound to each other, they quickly spread apart, causing significant expansion.
2.2. Weak Intermolecular Forces
Because forces between gas particles are extremely small, nothing holds them close. A small rise in temperature results in a large increase in volume.
3. Expansion of Gases at Constant Pressure (Charles’s Law)
If pressure is kept constant, the volume of a gas increases directly with temperature. This is known as Charles’s Law.
\( V \propto T \)
Here, temperature must be measured on the Kelvin scale.
3.1. Mathematical Form
\( \dfrac{V_1}{T_1} = \dfrac{V_2}{T_2} \)
This shows that if temperature increases, volume increases proportionally.
3.2. Everyday Examples
- Hot-air balloons rise because heating the air inside makes it expand and become lighter.
- A football left in the sun becomes harder because the air inside expands.
4. Expansion of Gases at Constant Volume (Pressure Law)
If the volume of a gas is kept constant (for example, in a sealed container), heating increases the pressure. This is because faster-moving particles hit the container walls more often and with greater force.
4.1. Mathematical Form
\( P \propto T \)
or
\( \dfrac{P_1}{T_1} = \dfrac{P_2}{T_2} \)
4.2. Everyday Examples
- Aerosol cans warn against heating because pressure increases and may cause bursting.
- A bicycle tyre becomes harder on a hot day because the air inside exerts more pressure.
5. Expansion of Gases at Constant Temperature (Boyle’s Law)
If temperature remains constant, gases obey Boyle’s Law. It states that the pressure of a gas is inversely proportional to its volume.
\( P \propto \dfrac{1}{V} \)
5.1. Mathematical Form
\( P_1V_1 = P_2V_2 \)
This means if volume decreases, pressure increases, and vice versa.
5.2. Everyday Examples
- Pressing a bicycle pump reduces air volume, increasing pressure to inflate the tyre.
- Deep-sea divers experience high pressure because water compresses the air in their bodies.
6. Coefficient of Expansion for Gases
For all ideal gases, the coefficient of volume expansion is the same when measured under the same conditions. This value is approximately:
\( \gamma_g \approx \dfrac{1}{273} \, \text{per °C} \)
This means that at constant pressure, a gas expands by about 1/273 of its volume at 0°C for every degree rise in temperature.
7. Why Gases Expand Uniformly
Unlike solids and liquids, gases expand uniformly in all directions because their particles are free to move. The expansion depends mainly on the balance between particle motion, pressure, and temperature.
7.1. Dependence on Pressure
At lower pressure, gas particles have more room to spread out, so expansion is more noticeable. At high pressure, expansion is restricted.
7.2. Dependence on Temperature Scale
For consistency, gas expansion is always calculated using temperatures in Kelvin because its zero point (absolute zero) is physically meaningful.
8. Everyday Examples of Expansion of Gases
- Air in car tyres expands on long drives, increasing pressure.
- A sealed plastic bottle may bulge if left in the sun.
- Heating air inside a room causes it to rise, creating convection currents.
- Balloons expand when brought into warm rooms because the air inside expands.