Pressure vs. Volume
Discovered by Robert Boyle in 1662, Boyle's Law is a fundamental experimental gas law that describes the inversely proportional relationship between the absolute pressure and volume of a gas, provided the temperature and the amount of gas remain perfectly constant.
The law simply states that if you squeeze a gas into half the space (decreasing its volume), its pressure will exactly double. Conversely, if you allow a gas to expand into a larger container, its pressure will drop.
The Mechanics of Breathing
You use Boyle's Law every single second of your life to breathe:
- Inhalation: Your diaphragm flexes downward, physically expanding the volume ($V$) of your chest cavity. According to Boyle's law, this increase in volume causes a decrease in pressure ($P$) inside your lungs. Because the pressure in your lungs is now lower than the atmospheric pressure outside, air violently rushes in through your mouth to equalize it.
- Exhalation: Your diaphragm relaxes, shrinking your chest cavity. The volume decreases, the internal pressure skyrockets above atmospheric pressure, and the air is pushed out.
- Deep Sea Diving: If a diver takes a full breath of compressed air at $30$ meters deep (where pressure is 4x higher) and holds their breath while swimming up, the decreasing external pressure will cause the air inside their lungs to expand massively according to Boyle's law, potentially rupturing their lungs.
The Formula
Example Calculation
A sealed syringe contains $10 , \text{Liters}$ of gas at exactly $100,000 , \text{Pa}$ ($1 , \text{atm}$). You forcefully push the plunger down until the volume is reduced to just $2 , \text{Liters}$.
- Multiply Initial State ($P_1 \cdot V_1$): $100,000 \cdot 10 = 1,000,000$.
- Divide by New Volume ($V_2$): $1,000,000 / 2 = 500,000 , \text{Pa}$.
The new pressure is $500,000 , \text{Pa}$ ($5 , \text{atm}$). Because you compressed the gas into 1/5th of its original space, the pressure increased by exactly 5 times.