What is the formula for final volume?

Decompressing the Calculation: Understanding Final Volume in Boyle’s Law

Boyle’s Law, a cornerstone of gas behavior, dictates that the pressure and volume of a gas are inversely proportional at a constant temperature. Understanding how to calculate the final volume after a pressure change is crucial in various applications, from understanding lung function to designing industrial processes. This article breaks down the calculation, using a real-world example and highlighting the importance of unit consistency.

The problem presented describes a gas initially occupying 0.001 m³ at a pressure of 101,325 Pa (Pascals, a unit of pressure). The pressure then decreases to 81,060 Pa, causing the gas to expand. The question is: how do we calculate this final volume?

Boyle’s Law is mathematically 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

To find the final volume (V₂), we simply rearrange the formula:

V₂ = (P₁V₁) / P₂

Now, let’s plug in the given values:

• P₁ = 101,325 Pa
• V₁ = 0.001 m³
• P₂ = 81,060 Pa

Therefore:

*V₂ = (101,325 Pa 0.001 m³) / 81,060 Pa**

V₂ ≈ 0.00125 m³

This confirms the stated final volume. The calculation is straightforward, highlighting the inverse relationship: as pressure decreases, volume increases proportionally.

The article then mentions a volume change (ΔV) of 250 cm³. This is simply the difference between the final and initial volumes:

ΔV = V₂ – V₁

Converting the volumes to cubic centimeters (1 m³ = 1,000,000 cm³):

• V₁ = 1000 cm³
• V₂ = 1250 cm³

ΔV = 1250 cm³ – 1000 cm³ = 250 cm³

This confirms the given volume change. The key takeaway is the importance of maintaining consistent units throughout the calculation. Using a consistent unit system, such as SI units (meters, Pascals), ensures accurate results. Inconsistency can lead to significant errors.

In conclusion, calculating the final volume under Boyle’s Law involves a simple yet powerful formula. By understanding the inverse relationship between pressure and volume and applying the formula correctly, we can accurately predict the volume changes in gases under varying pressure conditions. This understanding has far-reaching implications across various scientific and engineering disciplines.