Certainly! Let's solve this step-by-step.
### Formula:
The problem can be solved using Boyle's Law, which states that for a given mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. Mathematically, Boyle's Law is represented as:
\(\[ P_1 \times V_1 = P_2 \times V_2 \]\)
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.
### Input Numbers:
From the problem, we have:
- Initial pressure (\(\( P_1 \)\)): 8 Pa
- Initial volume (\(\( V_1 \)\)): 4 mL
- Final pressure (\(\( P_2 \)\)): 10 Pa
We are asked to find the final volume (\(\( V_2 \)\)).
### Solution:
1. Start with the Boyle's Law equation:
\(\[ P_1 \times V_1 = P_2 \times V_2 \]\)
2. Substitute the known values into the equation:
\(\[ 8 \, \text{Pa} \times 4 \, \text{mL} = 10 \, \text{Pa} \times V_2 \]\)
3. To solve for \(\( V_2 \)\), divide both sides of the equation by the final pressure (\(\( P_2 \)\)):
\(\[ V_2 = \frac{8 \, \text{Pa} \times 4 \, \text{mL}}{10 \, \text{Pa}} \]\)
4. Calculate the result:
\(\[ V_2 = \frac{32 \, \text{Pa} \cdot \text{mL}}{10 \, \text{Pa}} \]\)
\(\[ V_2 = 3.2 \, \text{mL} \]\)
### Answer:
The final volume (\(\( V_2 \)\)) would be 3.2 mL when the pressure rises to 10 Pa.
