Boyle's Law Application: Understanding Gas Pressure and Volume Relationships

Understanding the relationship between the pressure and volume of an ideal gas at a constant temperature is crucial in various scientific and engineering applications. This article delves into Boyle's Law and its application to determine the final pressure of a gas when it is compressed to a final volume.

Introduction to Boyle's Law

Boyle's Law, named after the Irish scientist Robert Boyle, describes the inverse relationship between the pressure and volume of an ideal gas at a constant temperature. Mathematically, it can be expressed as:

P1V1 P2V2

Where:

P1 is the initial pressure V1 is the initial volume P2 is the final pressure V2 is the final volume

Problem Setup and Solution

A given sample of gas at 0°C and 5 ATM occupies a volume of 75 L. The gas is then compressed to a final volume of 30 L. To find the final pressure, we can use Boyle's Law:

Solving with Direct Application of Boyle's Law

Given:

P1 5 ATM V1 75 L V2 30 L

Rearranging the equation for P2, we get:

P2 (P1V1) / V2

Substituting the known values:

P2 (5 ATM times; 75 L) / 30 L 12.5 ATM

Therefore, the final pressure P2 is 12.5 ATM.

Alternate Solution Using Ideal Gas Law

If we consider the ideal gas law, the equation becomes more comprehensive. The ideal gas law is:

P1V1/T1 P2V2/T2

At constant temperature (T1 T2), this simplifies to:

P1V1 P2V2

Using the same values as before:

P2 (P1V1) / V2

P2 (5 ATM times; 75 L) / 30 L 12.5 ATM

Thus, even when the temperature is considered, the final pressure remains the same at 12.5 ATM.

Conclusion

Boyle's Law and the ideal gas law both provide accurate solutions for understanding the behavior of gases under varying pressures and volumes. Both approaches yield the same result in this scenario, affirming the consistency and reliability of these fundamental principles in thermodynamics.

Additional Resources

For further learning, you may also explore the following:

Boyle's Law on Wikipedia Ideal Gas Law Explained at Khan Academy Boyle’s Law from LibreTexts