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 209. kpa. the piston is now pulled up, expanding the gas, until the gas has a final volume of 51.0 l. calculate the final pressure of the gas. round your answer to 3 significant digits.

Explanation:

Step1: Recall Boyle's Law formula

$P_1V_1 = P_2V_2$ (constant temperature)

Step2: Rearrange for final pressure $P_2$

$P_2 = \frac{P_1V_1}{V_2}$

Step3: Substitute values ($P_1=209$ kPa, $V_1=10.0$ L, $V_2=51.0$ L)

$P_2 = \frac{209 \times 10.0}{51.0} = \frac{2090}{51.0} \approx 40.98$

Step4: Round to 3 significant digits

$P_2 \approx 41.0$

Answer:

41.0 kPa