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:
[tex]\[ P_1 \times V_1 = P_2 \times V_2 \][/tex]
Where:
- [tex]\( P_1 \)[/tex] is the initial pressure.
- [tex]\( V_1 \)[/tex] is the initial volume.
- [tex]\( P_2 \)[/tex] is the final pressure.
- [tex]\( V_2 \)[/tex] is the final volume.
### Input Numbers:
From the problem, we have:
- Initial pressure ([tex]\( P_1 \)[/tex]): 8 Pa
- Initial volume ([tex]\( V_1 \)[/tex]): 4 mL
- Final pressure ([tex]\( P_2 \)[/tex]): 10 Pa
We are asked to find the final volume ([tex]\( V_2 \)[/tex]).
### Solution:
1. Start with the Boyle's Law equation:
[tex]\[ P_1 \times V_1 = P_2 \times V_2 \][/tex]
2. Substitute the known values into the equation:
[tex]\[ 8 \, \text{Pa} \times 4 \, \text{mL} = 10 \, \text{Pa} \times V_2 \][/tex]
3. To solve for [tex]\( V_2 \)[/tex], divide both sides of the equation by the final pressure ([tex]\( P_2 \)[/tex]):
[tex]\[ V_2 = \frac{8 \, \text{Pa} \times 4 \, \text{mL}}{10 \, \text{Pa}} \][/tex]
4. Calculate the result:
[tex]\[ V_2 = \frac{32 \, \text{Pa} \cdot \text{mL}}{10 \, \text{Pa}} \][/tex]
[tex]\[ V_2 = 3.2 \, \text{mL} \][/tex]
### Answer:
The final volume ([tex]\( V_2 \)[/tex]) would be 3.2 mL when the pressure rises to 10 Pa.
