At constant volume, pressure of a fixed amount of a gas varies directly with the temperature. It is the statement of which of the following laws ?

Question

Accepted Answer

The correct answer to the question is Option 3: Gay-Lussac's law. Let's delve into the reasoning behind this choice and why the other options are incorrect.

1. **Explanation for Option 3 (Gay-Lussac's Law):**
   - Gay-Lussac's law states that the pressure of a given mass of gas varies directly with the absolute temperature when the volume is kept constant. Mathematically, this can be expressed as $ P \propto T $ or $ \frac{P}{T} = \text{constant} $, where $ P $ is the pressure and $ T $ is the temperature in Kelvin. This law is applicable when the volume of the gas does not change, and it clearly aligns with the statement in the question that at constant volume, the pressure of a fixed amount of gas varies directly with the temperature.

2. **Why Option 1 (Boyle's Law) is Incorrect:**
   - Boyle's law describes the relationship between pressure and volume at constant temperature. It states that the pressure of a gas is inversely proportional to its volume when the temperature is held constant, expressed as $ PV = \text{constant} $. This law does not involve temperature as a variable affecting pressure, so it does not match the scenario described in the question.

3. **Why Option 2 (Charles's Law) is Incorrect:**
   - Charles's law focuses on the relationship between volume and temperature at constant pressure. It states that the volume of a gas is directly proportional to its absolute temperature when the pressure remains constant, expressed as $ V \propto T $. Since the question specifies a constant volume and a relationship between pressure and temperature, Charles's law is not applicable here.

4. **Why Option 4 (Avogadro's Law) is Incorrect:**
   - Avogadro's law deals with the relationship between the volume of a gas and the number of moles at constant temperature and pressure. It states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This law does not address the relationship between pressure and temperature, making it irrelevant to the question.

In conclusion, Gay-Lussac's law is the correct choice because it directly addresses the relationship between pressure and temperature at constant volume, which is precisely what the question describes.