In the combustion chamber of an engine the initial volume is 450cm^3 at a pressure of 1.0 atmosphere. If the piston displaces 402cm^3 of the total, what is the resulting pressure in the combustion chamber? (Assume negligible temperature change.) Hint: Calculate the new volume by subtracting the amount of space the piston takes up from the initial volume. square atm

To solve this problem, we can use Boyle's Law, which states that for a given mass of gas at constant temperature, the pressure and volume are inversely proportional. Mathematically, Boyle's Law is expressed as:<br /><br />\[ P_1 V_1 = P_2 V_2 \]<br /><br />where:<br />- \( P_1 \) is the initial pressure,<br />- \( V_1 \) is the initial volume,<br />- \( P_2 \) is the final pressure,<br />- \( V_2 \) is the final volume.<br /><br />Given:<br />- Initial volume, \( V_1 = 450 \, \text{cm}^3 \)<br />- Initial pressure, \( P_1 = 1.0 \, \text{atm} \)<br />- Volume displaced by the piston, \( V_{\text{displaced}} = 402 \, \text{cm}^3 \)<br /><br />First, calculate the new volume \( V_2 \):<br /><br />\[ V_2 = V_1 - V_{\text{displaced}} \]<br />\[ V_2 = 450 \, \text{cm}^3 - 402 \, \text{cm}^3 \]<br />\[ V_2 = 48 \, \text{cm}^3 \]<br /><br />Now, apply Boyle's Law to find the resulting pressure \( P_2 \):<br /><br />\[ P_1 V_1 = P_2 V_2 \]<br />\[ (1.0 \, \text{atm}) \times (450 \, \text{cm}^3) = P_2 \times (48 \, \text{cm}^3) \]<br /><br />Solve for \( P_2 \):<br /><br />\[ P_2 = \frac{(1.0 \, \text{atm}) \times (450 \, \text{cm}^3)}{48 \, \text{cm}^3} \]<br />\[ P_2 = \frac{450}{48} \, \text{atm} \]<br />\[ P_2 \approx 9.375 \, \text{atm} \]<br /><br />Therefore, the resulting pressure in the combustion chamber is approximately \( 9.375 \, \text{atm} \).