To solve for the new pressure experienced by the piston when the volume of the chamber is reduced from 4.7 liters to 1.0 liter, we can use Boyle's Law. Boyle's Law states that for a given amount of gas at constant temperature, the pressure and volume of the gas are inversely proportional. Mathematically, this 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
Given the following values:
- Initial volume ([tex]\( V_1 \)[/tex]) = 4.7 liters
- Initial pressure ([tex]\( P_1 \)[/tex]) = 3.1 atmospheres
- Final volume ([tex]\( V_2 \)[/tex]) = 1.0 liter
We need to find the final pressure ([tex]\( P_2 \)[/tex]). We can rearrange the equation to solve for [tex]\( P_2 \)[/tex]:
[tex]\[ P_2 = \frac{P_1 \times V_1}{V_2} \][/tex]
Substitute the given values into the equation:
[tex]\[ P_2 = \frac{3.1 \, \text{atm} \times 4.7 \, \text{L}}{1.0 \, \text{L}} \][/tex]
Now calculate the result:
[tex]\[ P_2 = \frac{14.57 \, \text{atm} \cdot \text{L}}{1.0 \, \text{L}} \][/tex]
[tex]\[ P_2 = 14.57 \, \text{atm} \][/tex]
Therefore, the new pressure experienced by the piston when the volume of the chamber is reduced to 1.0 liter is 14.57 atmospheres.
