Temperature vs. Volume
Charles's Law (also known as the law of volumes) is an experimental gas law which describes how gases tend to physically expand when heated. It states that if the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be directly proportional.
As the temperature of a gas increases, the gas molecules gain kinetic energy and move much faster. To maintain a constant pressure against the walls of their container, they must spread further apart, physically expanding the volume of the gas.
Real-World Heating
- Hot Air Balloons: This is the most famous application. A burner violently heats the air inside the balloon's envelope. According to Charles's law, the heated air expands. Since it now occupies a larger volume for the exact same mass, its density decreases. The balloon becomes less dense than the cold air around it, and buoyancy lifts it into the sky.
- Tires in Winter: If you inflate your car tires to the perfect pressure during a hot summer day, you will often trigger a 'Low Tire Pressure' warning on the first freezing morning of winter. The cold temperature causes the volume of the air inside the tire to shrink.
- Baking Bread: Yeast produces pockets of carbon dioxide gas inside dough. When placed in a hot oven, Charles's Law dictates that these gas bubbles will expand rapidly due to the heat, causing the bread to rise and become fluffy.
The Formula
Example Calculation
A perfectly elastic balloon contains $5 , \text{Liters}$ of air at a room temperature of $300 , \text{K}$ (about $27^\circ\text{C}$). You place it in a hot oven at $600 , \text{K}$.
- Divide Initial Volume by Initial Temp ($V_1 / T_1$): $5 / 300 = 0.01666...$
- Multiply by New Temp ($T_2$): $0.01666... \cdot 600 = 10 , \text{Liters}$.
Because you exactly doubled the absolute temperature (from 300K to 600K), the volume of the balloon perfectly doubled to $10 , \text{Liters}$.