The graph of pressure (P) against the reciprocal of the volume (I/V) in Boyles's law is a?

1. Analyze the Question

The question asks for the shape of the graph obtained when plotting Pressure ($P$) against the reciprocal of volume ($1/V$) based on Boyle’s Law.

2. Explain the Concept

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 ($V$):

To express this as an equation, we introduce a constant ($k$):

This equation follows the mathematical form of a linear equation, $y = mx + c$, where:

• $y$ is the pressure ($P$)
• $x$ is the reciprocal of volume ($1/V$)
• $m$ (the gradient) is the constant ($k$)
• $c$ (the intercept) is $0$

3. Show the Solution

• If you plot $P$ against $V$, you get a hyperbola (because $P$ decreases as $V$ increases).
• However, if you plot $P$ against $1/V$, you are essentially plotting $y$ against $x$ in a direct proportion relationship.
• Since $P = k(1/V)$, as $1/V$ increases, $P$ increases at a constant rate.
• A graph of a direct proportion ($y = mx$) always results in a straight line passing through the origin.

4. Identify the Answer

The graph of $P$ against $1/V$ is a straight line. Therefore, the correct option is D.

5. Exam Tip

• Memory Trick: Remember the "Boyle's Law Graph Rule": • $P$ vs $V$ = Hyperbola (Curve) • $P$ vs $1/V$ = Straight line • $PV$ vs $P$ = Straight horizontal line (because $PV$ is constant)
• Always check the axes labels carefully in the exam hall; a small change in the variable (like $1/V$ vs $V$) completely changes the shape of the graph!