Question

match one graph shown at right to each of the gas laws named below. charles’s law gay-lussac’s law boyle’s law done a) v t b) p t c) p t d) v t e) p v

Explanation:

Step1: Recall Charles's Law

Charles's Law states that at constant pressure, the volume \( V \) of a gas is directly proportional to its absolute temperature \( T \) (\( V \propto T \) when \( P \) is constant). So the graph of \( V \) vs \( T \) should be a straight line passing through the origin. Among the graphs, graph d ( \( V \) vs \( T \) with a straight line through origin) matches Charles's law.

Step2: Recall Gay - Lussac's Law

Gay - Lussac's Law states that at constant volume, the pressure \( P \) of a gas is directly proportional to its absolute temperature \( T \) (\( P \propto T \) when \( V \) is constant). So the graph of \( P \) vs \( T \) should be a straight line passing through the origin. Among the graphs, graph b ( \( P \) vs \( T \) with a straight line through origin) matches Gay - Lussac's law.

Step3: Recall Boyle's Law

Boyle's Law states that at constant temperature, the pressure \( P \) of a gas is inversely proportional to its volume \( V \) (\( P\propto\frac{1}{V} \) when \( T \) is constant). So the graph of \( P \) vs \( V \) should be a hyperbola. Among the graphs, graph e ( \( P \) vs \( V \) with a hyperbolic curve) matches Boyle's law.

Answer:

Charles’s law: d) \( V \) vs \( T \) (straight line through origin)
Gay - Lussac’s law: b) \( P \) vs \( T \) (straight line through origin)
Boyle’s law: e) \( P \) vs \( V \) (hyperbolic curve)