Question

1. which of the following graphs best represents the relationship between the pressure and volume of an ideal gas at constant temperature?

Explanation:

Step1: Recall Boyle's law

For an ideal gas at constant temperature, $PV = k$ (where $k$ is a constant), so $P=\frac{k}{V}$. This is an inverse - relationship.

Step2: Analyze the graph of an inverse - relationship

The graph of a function $y = \frac{a}{x}$ ($a>0$) is a hyperbola. As $x$ (in this case $V$) increases, $y$ (in this case $P$) decreases.

Answer:

The first graph (the hyperbola - shaped curve showing that as $V$ increases, $P$ decreases) best represents the relationship between the pressure and volume of an ideal gas at constant temperature.