2021 A/L Physics Past Paper · Question 19 (English Medium)

Answer: (5) Graph (5)

What the question asks

We want: the graph of the product $PV$ against $P$, for a fixed mass of gas at constant temperature.

What each letter means:

$P$ ($\text{Pa}$): pressure, how hard the gas pushes on the walls.

$V$ ($\text{m}^3$): volume, the space the gas fills.

$PV$ ($\text{J}$): the product of pressure and volume.

Relevant theory

The pressure of a fixed mass of a gas is inversely proportional to its volume, provided the temperature remains constant.

Required equations

$P \propto \dfrac{1}{V}$

$PV = \text{constant}$

Reasoning and calculation

For example, close the nozzle of a bicycle pump with your finger and push the plunger in slowly.

The air has less room, so the volume $V$ gets smaller.

The air pushes back harder, so the pressure $P$ gets bigger.

If the room is halved, the push is doubled. $V$ falls by the same factor that $P$ rises.

$$PV = \text{constant}$$

In words: pressure $\times$ volume stays the same, however hard you push.

So when $PV$ is drawn against $P$, the line stays at the same height.

What is on the axes?

Across: the pressure $P$. Up: the product $PV$.

What happens as $P$ rises?

If $P$ doubles, $V$ halves. The product $PV$ stays the same.

So for every value of $P$ the height of the graph is the same.

Compare the five graphs. In (1) and (4) $PV$ falls. In (2) and (3) $PV$ rises.

Only in graph (5) does $PV$ stay at the same height for every $P$. It is a horizontal line.

The answer is (5).

Checks

$a * b$

Does it make sense?

The unit of $PV$ is $\text{Pa} \times \text{m}^3 = \text{J}$, an energy. At a fixed temperature the energy of the gas does not change, so $PV$ should not change either.

Conclusion

$PV = \text{constant}$

$PV$ is constant at constant temperature, so the graph is a horizontal line.

The answer is (5).

Read the axes first. Graph (1) is the shape of $P$ against $V$, a common trap.

For $PV$ against $P$ at constant temperature, the line is flat.

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