Solving a Pressure and Volume Problem using Boyle's Law
Understanding Boyle's Law in Gas Physics
Boyle's Law is a fundamental principle in gas physics that describes the relationship between the pressure and volume of a gas. According to Boyle's Law, the pressure of a gas is inversely proportional to its volume, as long as the temperature remains constant.
Applying Boyle's Law to a Snorkeling Scenario
Imagine a snorkeler who takes a syringe filled with 18 mL of air from the surface, where the pressure is 1.0 atm, to an unknown depth. At this depth, the volume of the air in the syringe decreases to 8 mL. The goal is to determine the pressure at this unknown depth.
Solution: Finding the Pressure at the Unknown Depth
Given: Initial volume (V1) = 18 mL, Final volume (V2) = 8 mL, Initial pressure (P1) = 1.0 atm
We can use Boyle's Law, which states: P1 * V1 = P2 * V2
Substitute the given values into the formula:
P2 = (P1 * V1) / V2
Calculate the pressure at the unknown depth:
The pressure at the unknown depth is 2.25 atm.
Conclusion
Through the application of Boyle's Law, we were able to determine the pressure at the unknown depth in the snorkeling scenario. Understanding the relationship between pressure and volume of a gas is crucial in various scientific and practical applications.
A snorkeler takes a syringe filled with 18 mL of air from the surface, where the pressure is 1.0 atm to an unknown depth. The volume of the air in the syringe at this depth is 8 mL. What is the pressure at the unknown depth? The pressure at the unknown depth is 2.25 atm. Explanation:To solve this problem, we can use Boyle's Law, which relates the pressure and volume of a gas. Boyle's Law states that the pressure of a gas is inversely proportional to its volume, assuming the temperature remains constant.We are given that the initial volume of air in the syringe is 18 mL and the final volume at the unknown depth is 8 mL. Let's denote the initial pressure as P1 and the final pressure as P2.According to Boyle's Law, P1V1 = P2V2. Plugging in the given values, we have:P1 * 18 mL = P2 * 8 mLTo find the pressure at the unknown depth, we can rearrange the equation:P2 = (P1 * 18 mL) / 8 mLNow, we can substitute the given value of P1, which is 1.0 atm:P2 = (1.0 atm * 18 mL) / 8 mLSimplifying the equation, we get:P2 = 2.25 atmTherefore, the pressure at the unknown depth is 2.25 atm.