75. Pressure & Volume (pV = constant)

This video explains the relationship between the pressure and volume of a gas at a constant temperature, a principle often referred to as Boyle's Law.

1. The Relationship

Pressure and volume are inversely proportional. This means:

• As volume increases, pressure decreases.

• As volume decreases, pressure increases.

For a fixed mass of gas at a constant temperature, the pressure multiplied by the volume will always equal a constant value:

$P \times V = \text{constant}$

2. Using the Equation in Calculations

There are two common ways to solve problems using this relationship:

Method A: Finding the Constant

1. Calculate the constant for the initial state (P₁ \times V₁).

2. Use that constant to find the missing value in the second state (P₂ x V₂ = constant)

Method B: The Comparison Formula

You can set the two states equal to each other:

$P_1 \times V_1 = P_2 \times V_2$

• P₁, V₁: Initial pressure and volume.

• P₂, V₂: Final pressure and volume.

3. Example Calculation

Question: A gas occupies 1.5m³ at a pressure of 100Pa. Calculate the pressure if it is compressed to 0.3m³.

1. Identify values: P₁ = 100Pa V₁ = 1.5m³, V₂ = 0.3m³.

2. Apply formula: 100 × 1.5 = P₂ x 0.3.

3. Solve: $150 = P₂ × 0.3 $⇒$ P₂ = $\frac{150}{0.3}$

4. Result: 500 Pa.

4. Important Notes

• Units: You can use any units for pressure (e.g., Pa, kPa) and volume (e.g., m³, Liters), provided you use the same units on both sides of the equation.

• Assumptions: These equations only work if the temperature and the mass of the gas remain constant.

5. Summary Table