Examples of Boyle's Law Calculation Example

Introduction to Boyle’s Law

Boyle’s Law states that the pressure of a gas is inversely proportional to its volume when the temperature is held constant. This fundamental principle of gas behavior is crucial in various scientific and engineering applications. Understanding how to apply Boyle’s Law can help in calculating changes in gas pressure or volume in real-world situations.

Example 1: Inflating a Balloon

In this example, we explore how Boyle’s Law applies when inflating a balloon. When you blow air into a balloon, you increase the volume of the air inside, which affects the pressure. Let’s say the initial volume of the balloon is 2 liters at a pressure of 1 atm. If we want to know the pressure after inflating it to 1 liter, we can use Boyle’s Law.

Using the formula:

P1 × V1 = P2 × V2
Where:

• P1 = Initial Pressure (1 atm)
• V1 = Initial Volume (2 L)
• P2 = Final Pressure
• V2 = Final Volume (1 L)

Calculating for P2:
P2 = (P1 × V1) / V2
P2 = (1 atm × 2 L) / 1 L
P2 = 2 atm

So, after inflating the balloon to a volume of 1 liter, the pressure inside the balloon rises to 2 atm.

Notes

• This example illustrates the direct application of Boyle’s Law in everyday activities.
• The assumption here is that temperature remains constant during the inflation process.

Example 2: Syringe and Gas Compression

Consider a medical syringe used to inject medication. If the volume of the syringe decreases while the amount of gas inside remains constant, the pressure will increase. Let’s say the initial volume of the gas in the syringe is 50 mL at a pressure of 1 atm. If the volume is reduced to 25 mL, we can find the new pressure using Boyle’s Law.

Using the formula:
P1 × V1 = P2 × V2
Where:

• P1 = Initial Pressure (1 atm)
• V1 = Initial Volume (50 mL)
• P2 = Final Pressure
• V2 = Final Volume (25 mL)

Calculating for P2:
P2 = (P1 × V1) / V2
P2 = (1 atm × 50 mL) / 25 mL
P2 = 2 atm

Thus, the pressure in the syringe increases to 2 atm when the volume is halved.

Notes

• This example is particularly relevant in the medical field for understanding how gas pressures work in syringes.
• It’s important to maintain a constant temperature for accurate calculations.

Example 3: Diving and Boyle’s Law

Diving is a practical scenario where Boyle’s Law is crucial for safety. As a diver descends underwater, the pressure increases due to the weight of the water above. If a diver starts at a depth where the pressure is 2 atm and the volume of air in their lungs is 6 liters, we can calculate the volume at a depth where the pressure is 4 atm.

Using the formula:
P1 × V1 = P2 × V2
Where:

• P1 = Initial Pressure (2 atm)
• V1 = Initial Volume (6 L)
• P2 = Final Pressure (4 atm)
• V2 = Final Volume

Calculating for V2:
V2 = (P1 × V1) / P2
V2 = (2 atm × 6 L) / 4 atm
V2 = 3 L

At a pressure of 4 atm, the volume of air in the diver’s lungs decreases to 3 liters.

Notes

• This example highlights the importance of Boyle’s Law for divers to prevent lung over-expansion during ascent.
• The calculations assume a consistent temperature, which is generally valid for short timeframes in water.