Question

A gas has a volume of 3.4 L at 298 K. What is the final temperature if the volume of gas increases to 6.8 L?

• A. 596 K
• B. 412 K
• C. 298 K
• D. 149 K

Hint:

Charles's Law represents a direct linear scaling relationship. Since the volume doubles perfectly from 3.4 L to 6.8 L, the absolute temperature must also double perfectly. Simply compute $298 \times 2 = 596$ to find the answer instantly without writing down formulas.

Answer 1

The Correct Option is A

Step 1: Spot the fixed and changing quantities.
Pressure and amount of gas are held constant while volume and temperature change. That is the signature of Charles's Law.
Step 2: Write Charles's Law.
At constant pressure, volume is directly proportional to absolute temperature, so $\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2}$.
Step 3: List the given data.
$V_1 = 3.4\text{ L}$, $T_1 = 298\text{ K}$, $V_2 = 6.8\text{ L}$, and $T_2$ is unknown.
Step 4: Notice the simple ratio.
$\dfrac{V_2}{V_1} = \dfrac{6.8}{3.4} = 2$, so the volume has exactly doubled.
Step 5: Apply direct proportionality.
Since $V \propto T$ at constant pressure, doubling the volume must double the absolute temperature.
Step 6: Compute the final temperature.
$T_2 = 2 \times T_1 = 2 \times 298 = 596\text{ K}$.
\[ \boxed{T_2 = 596\text{ K, option (1)}} \]