According to Boyle's Law, how are the pressure and volume of a gas related at constant temperature?

• A. Pressure and volume both increase together.
• B. Pressure and volume are unrelated.
• C. Pressure and volume are directly proportional.
• D. Pressure and volume are inversely proportional.

Answer: (D)

Verified step by step guidance

1. Recall Boyle's Law, which describes the relationship between pressure and volume of a gas at constant temperature.
2. Boyle's Law states that the product of pressure (P) and volume (V) is a constant when temperature and amount of gas are held constant, expressed as \(P \times V = k\).
3. This means that if the volume increases, the pressure must decrease to keep the product constant, and vice versa.
4. Therefore, pressure and volume are inversely proportional, which can be mathematically written as \(P \propto \frac{1}{V}\) or \(P = \frac{k}{V}\).
5. This inverse relationship explains why pressure and volume do not both increase together, nor are they unrelated or directly proportional.