Question

a cylinder with a moveable piston contains 3.5 l of gas at 310 k and 2.5 atm. if the temperature increases to 350 k and the pressure drops to 1.5 atm, what is the new volume of the system?

Explanation:

Step1: Recall combined gas law

The combined gas law is $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$, where $P$ = pressure, $V$ = volume, $T$ = temperature (Kelvin).

Step2: Identify known values

$P_1=2.5$ atm, $V_1=3.5$ L, $T_1=310$ K, $P_2=1.5$ atm, $T_2=350$ K, solve for $V_2$.

Step3: Rearrange formula for $V_2$

$V_2 = \frac{P_1V_1T_2}{P_2T_1}$

Step4: Substitute values into formula

$V_2 = \frac{(2.5)(3.5)(350)}{(1.5)(310)}$

Step5: Calculate the result

$V_2 = \frac{2975}{465} \approx 6.4$ L

Answer:

6.4 L