Question

Calculate the new pressure of the gas enclosed in a cylinder when it compressed from 5 L to 2 L at 1 atm and 300 K. The final temperature in this process is 500 K.

• A. \(1.5\) atm
• B. \(3.12\) atm
• C. \(2.5\) atm
• D. \(4.16\) atm

Hint:

Use the combined gas law P1V1/T1 = P2V2/T2 with the final temperature of 500 K.

Answer 1

The Correct Option is D

Step 1: Plan
The amount of gas is fixed, so $PV/T$ stays constant.

Step 2: Substitute
$P_2 = \dfrac{P_1 V_1 T_2}{T_1 V_2} = \dfrac{1 \times 5 \times 500}{300 \times 2} = \dfrac{2500}{600}$.

Step 3: Result
$2500/600 = 4.17$, which matches the given 4.16 atm. Ignoring T (Boyle only) would give 2.5 atm, so (C) is a trap.

Final Answer:
Option (D), 4.16 atm. \[ \boxed{4.16 \text{ atm}} \]