To solve this problem, we will use 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 expressed as:
[tex]\[ P_1 \times V_1 = P_2 \times V_2 \][/tex]
Here:
- [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.
We are given:
- Initial volume, [tex]\( V_1 = 4.23 \)[/tex] liters,
- Initial pressure, [tex]\( P_1 = 285 \)[/tex] kPa,
- Final volume, [tex]\( V_2 = 11.03 \)[/tex] liters.
We need to find the final pressure [tex]\( P_2 \)[/tex]. Rearranging the equation 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]\[ P_2 = \frac{285 \times 4.23}{11.03} \][/tex]
When we carry out the calculation:
[tex]\[ P_2 = \frac{1205.55}{11.03} \][/tex]
[tex]\[ P_2 \approx 109.3 \][/tex]
Thus, the pressure in the container after expansion, with the temperature held constant, is approximately 109.3 kPa.
