Question

What would be the final volume of a balloon that starts at a pressure of 50kPa and a volume of 2.1 L
Assume the final pressure of the balloon is 100 kPa.

Boyle law equation.

Answer 1

Boyle's Law states that the pressure and volume of a gas have an inverse relationship when temperature is held constant. The mathematical expression of Boyle's Law is:

\[
P_1 V_1 = P_2 V_2
\]

Where:
- \( P_1 \) is the initial pressure,
- \( V_1 \) is the initial volume,
- \( P_2 \) is the final pressure,
- \( V_2 \) is the final volume.

Given:
- \( P_1 = 50 \, \text{kPa} \)
- \( V_1 = 2.1 \, \text{L} \)
- \( P_2 = 100 \, \text{kPa} \)

We need to find \( V_2 \). Rearranging the formula to solve for \( V_2 \):

\[
V_2 = \frac{P_1 V_1}{P_2}
\]

Now, substituting the values:

\[
V_2 = \frac{50 \, \text{kPa} \times 2.1 \, \text{L}}{100 \, \text{kPa}}
\]

Calculating:

\[
V_2 = \frac{105 \, \text{kPa} \cdot \text{L}}{100 \, \text{kPa}} = 1.05 \, \text{L}
\]

Therefore, the final volume of the balloon when the pressure is increased to 100 kPa is **1.05 L**.