A fixed mass of gas is kept at a constant temperature. Its pressure, p, is measured for several different volumes, V, and a graph of p (on the y-axis) against 1/V (on the x-axis) is plotted. What is the shape of this graph?

Answer: A. Step 1: Start from the pressure–volume law For a fixed mass of gas at constant temperature: pV = constant, call it k Step 2: Rearrange in terms of 1/V Dividing both sides by V: p = k × 1/V Step 3: Recognise the form of this equation This h…

IGCSE Physics 0625: Graph of Pressure Against 1/Volume

Step 1: Start from the pressure–volume law

For a fixed mass of gas at constant temperature:

$pV = \text{constant}, \quad \text{call it } k$

Step 2: Rearrange in terms of $\dfrac{1}{V}$

Dividing both sides by $V$ :

$p = k \times \frac{1}{V}$

Step 3: Recognise the form of this equation

This has the form $p = k \times x$ , where $x = \dfrac{1}{V}$ , a straight-line equation ( $y = mx$ ) with gradient $k$ and no constant term added on. A graph of $p$ against $\dfrac{1}{V}$ is therefore a straight line whose gradient equals the constant $k$ ( $=pV$ ), and which passes through the origin, because when $\dfrac{1}{V} = 0$ , $p = 0$ .

Step 4: Match to the options

This matches option A.

Why the other options are wrong

Option	Problem
B	The equation $p = k \times (1/V)$ has no added constant, so the line must pass through the origin, not miss it.
C	A curve approaching both axes is the shape of $p$ plotted directly against $V$ (not against $1/V$ ).
D	A horizontal line would mean pressure never changes with volume, which contradicts $pV = \text{constant}$ .

Final answers

A graph of $p$ against $\dfrac{1}{V}$ for a fixed mass of gas at constant temperature is a straight line through the origin, option A.