The volume of a fixed mass of gas at 0º C is 200 m$^3$. What is its volume at 273º C at constant pressure?

1. Analyze the question

We are given the initial volume ($V_1$) and initial temperature ($T_1$) of a fixed mass of gas. We need to find the final volume ($V_2$) at a new temperature ($T_2$), assuming the pressure remains constant.

2. Explain the concept

This problem is governed by Charles's Law, which states that for a fixed mass of gas at constant pressure, the volume is directly proportional to its absolute temperature (measured in Kelvin).

The formula is:

Important Note: In gas law calculations, temperatures must always be converted from Celsius (°C) to Kelvin (K) by adding 273.

3. Show the solution

Step 1: Identify the given values

• $V_1 = 200 \text{ m}^3$
• $T_1 = 0^\circ\text{C} = 0 + 273 = 273 \text{ K}$
• $T_2 = 273^\circ\text{C} = 273 + 273 = 546 \text{ K}$
• $V_2 = ?$

Step 2: Substitute into the formula

Step 3: Solve for $V_2$

Since $546$ is exactly $2 \times 273$:

4. Identify the answer

The calculated volume is $400 \text{ m}^3$, which corresponds to option B.

5. Tip

Exam Strategy: Whenever you see a temperature in Celsius in a gas law problem, immediately add 273 to it before doing any calculations. Also, notice that when the absolute temperature doubles (from 273 K to 546 K), the volume must also double (from 200 to 400) because they are directly proportional!