Question

a cylinder is filled with 10.0 l of gas and a piston is put into it. the initial pressure of the gas is measured to be 287. kpa. the piston is now pulled up, expanding the gas, until the gas has a final volume of 48.0 l. calculate the final pressure of the gas. round your answer to 3 significant digits.

Explanation:

Step1: Identify the gas law

This is a Boyle's Law problem, which states that for a fixed amount of gas at constant temperature, \( P_1V_1 = P_2V_2 \).

Step2: List the given values

\( P_1 = 287 \, \text{kPa} \), \( V_1 = 10.0 \, \text{L} \), \( V_2 = 48.0 \, \text{L} \), and we need to find \( P_2 \).

Step3: Rearrange the formula to solve for \( P_2 \)

From \( P_1V_1 = P_2V_2 \), we get \( P_2=\frac{P_1V_1}{V_2} \).

Step4: Substitute the values into the formula

\( P_2=\frac{287 \, \text{kPa} \times 10.0 \, \text{L}}{48.0 \, \text{L}} \)

Step5: Calculate the result

\( P_2=\frac{2870}{48.0} \approx 59.8 \, \text{kPa} \)

Answer:

\( 59.8 \, \text{kPa} \)