Volume of Gas & Charles’s Law

Key Principle: Charles's Law

Charles’s Law describes how the volume of a fixed amount of gas changes in direct proportion to its absolute temperature when the pressure remains constant.

• When temperature (in Kelvin) increases, gas particles move faster, collide with the container walls more vigorously, and push outward.
  • Result: Volume expands.
• When temperature decreases, particle motion slows, collisions weaken, and the gas contracts.
  • Result: Volume shrinks.

Mathematical Relationship

At constant pressure and with a fixed quantity of gas:

${\frac{V<em>1}{T</em>1}=\frac{V<em>2}{T</em>2}}$

Where:

• $V<em>1, V</em>2$ = initial and final volumes (in $\text{L}$ or $\text{m}^3$)
• $T<em>1, T</em>2$ = initial and final absolute temperatures (in $\text{K}$)

Re-arranged forms frequently used:

• $V \propto T$ (volume is directly proportional to temperature)
• $V = kT$ where $k$ is a constant for a given amount of gas at constant pressure.

Experimental Demonstration: Balloon in Hot vs. Cold Water

1. Setup
   • A flexible gas balloon is immersed alternately in two baths: one of hot water and one of cold water.
2. Hot Water Phase
   • Temperature rise → gas molecules accelerate → balloon inflates.
   • Visual confirmation: balloon visibly enlarges.
3. Cold Water Phase
   • Temperature drop → molecular motion slows → balloon deflates.
   • Visual confirmation: balloon contracts.

Conceptual Takeaways & Real-World Relevance

• Weather balloons, car tires, and lungs all exhibit Charles’s Law: they expand in heat and contract in cold.
• Engineers account for thermal expansion of gases in designing engines, HVAC systems, and pressurized containers.
• Safety note: Over-inflated balloons in hot environments can burst as volume increases beyond elastic limits.