Question

At $0^\circ\text{C}$ a gas occupies 22.4 liters. What is the temperature in Kelvin to reach the volume of 224 liters?

• A. 546 K
• B. 273 K
• C. 2730 K
• D. 5460 K

Hint:

Logic Tip: Because volume and absolute temperature are directly proportional, if the volume increases by a factor of 10 ($22.4 \rightarrow 224$), the temperature in Kelvin must also increase by exactly a factor of 10 ($273 \rightarrow 2730$). No complex calculation needed!

Answer 1

The Correct Option is C

Concept:
Charles's Law states that at constant pressure, the volume of a fixed mass of a gas is directly proportional to its absolute temperature (in Kelvin). $$V \propto T \implies \frac{V_1}{T_1} = \frac{V_2}{T_2}$$
Step 1: Identify the initial and final states of the gas.
Initial volume, $V_1 = 22.4\text{ L}$ Initial temperature, $T_1 = 0^\circ\text{C}$. We must convert this to absolute temperature (Kelvin): $$T_1 = 0 + 273 = 273\text{ K}$$ Final volume, $V_2 = 224\text{ L}$ Final temperature, $T_2 = ?$
Step 2: Apply Charles's Law to find $T_2$.
Substitute the values into the formula: $$\frac{22.4}{273} = \frac{224}{T_2}$$ Rearrange the equation to isolate $T_2$: $$T_2 = \frac{224 \times 273}{22.4}$$
Step 3: Calculate the final temperature.
Notice that $224$ is exactly $10$ times $22.4$: $$T_2 = 10 \times 273$$ $$T_2 = 2730\text{ K}$$