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 190. kpa. the piston is now pushed down, compressing the gas, until the gas has a final volume of 8.70 l. calculate the final pressure of the gas. round your answer to 3 significant digits.

Explanation:

Step1: Apply Boyle's Law

Boyle's Law: $P_1V_1 = P_2V_2$
Given $P_1=190\ \text{kPa}$, $V_1=10.0\ \text{L}$, $V_2=8.70\ \text{L}$

Step2: Solve for $P_2$

Rearrange formula: $P_2 = \frac{P_1V_1}{V_2}$

Step3: Calculate final pressure

$P_2 = \frac{190 \times 10.0}{8.70} \approx 218.39\ \text{kPa}$

Step4: Round to 3 significant digits

$P_2 \approx 218\ \text{kPa}$

Answer:

218 kPa