JAMB 2021 Physics · Question 4

A gas at a volume of V 0 in a container at pressure p 0 is compressed to one-fifth of its volume. What will be…

Question

A gas at a volume of V $_{0}$ in a container at pressure p $_{0}$ is compressed to one-fifth of its volume. What will be its pressure if the magnitude of its original temperature T is constant?

A. $\frac{p_{0}} {5}$
B. $\frac{4p_{0}}{5}$
C.p $_{0}$
D.5P $_{0}$

Answer: D. 5P $_{0}$

Explanation written with AI and checked against the answer key

1. Analyze the question

We are given an initial state of a gas with volume $V_0$ and pressure $p_0$ . The gas is compressed to a new volume which is $\frac{1}{5}$ of the original volume. We are told the temperature $T$ remains constant. We need to find the new pressure.

2. Explain the concept

This problem involves Boyle’s Law. Boyle’s Law states that for a fixed mass of an ideal gas at a constant temperature, the pressure ( $p$ ) is inversely proportional to the volume ( $V$ ).

The mathematical expression is:

p_1V_1 = p_2V_2

Where:

$p_1$ and $V_1$ are the initial pressure and volume.
$p_2$ and $V_2$ are the final pressure and volume.

3. Show the solution

Initial state: • Pressure = $p_0$ • Volume = $V_0$
Final state: • Pressure = $p_2$ (what we need to find) • Volume = $\frac{1}{5}V_0$

Using the Boyle’s Law formula:

p_0 \times V_0 = p_2 \times \left(\frac{V_0}{5}\right)

To solve for $p_2$ , divide both sides by $\frac{V_0}{5}$ :

p_2 = \frac{p_0 \times V_0}{\frac{V_0}{5}}

The $V_0$ terms cancel out:

p_2 = p_0 \times 5

p_2 = 5p_0

4. Identify the answer

Comparing our result ( $5p_0$ ) to the given options, it matches option D.

5. Exam Tip

Whenever you see "constant temperature" in a gas law question, immediately think of Boyle's Law. A quick mental shortcut: if the volume is divided by a number (like 5), the pressure must be multiplied by that same number because they are inversely proportional.

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