A given mass of gas occupies 2dm3 at 300k. At what temperature will its volume be doubled, keeping the pressure constant?

1. Analyze the question

We are given the initial volume ($V_1$) and initial temperature ($T_1$) of a gas. We need to find the new temperature ($T_2$) when the volume is doubled ($V_2 = 2 \times V_1$), while the pressure remains constant.

2. Explain the concept

This problem is governed by Charles's Law. Charles's Law 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:

3. Show the solution

• Step 1: Identify the given values • $V_1 = 2 \text{ dm}^3$ • $T_1 = 300 \text{ K}$ • $V_2 = 2 \times V_1 = 2 \times 2 = 4 \text{ dm}^3$ • $T_2 = ?$

• Step 2: Substitute the values into the formula $$\frac{2}{300} = \frac{4}{T_2}$$

• Step 3: Solve for $T_2$ Cross-multiply to isolate $T_2$: $$2 \times T_2 = 4 \times 300$$ $$2 \times T_2 = 1200$$ $$T_2 = \frac{1200}{2}$$ $$T_2 = 600 \text{ K}$$

4. Identify the answer

Comparing our result ($600 \text{ K}$) with the given options, the correct choice is D.

5. Tip

Whenever you see "constant pressure" in a gas law problem, immediately think of Charles's Law. A quick mental shortcut: if the pressure is constant, doubling the volume will always require doubling the absolute temperature. Since $300 \text{ K} \times 2 = 600 \text{ K}$, you can solve this in seconds!