At constant temperature, the product of pressure and volume of a given amount of a gas is constant. This is :

Options

A. Gay-Lussac law
B. Charles's law
C. Boyle's law
D. None of these.

Answer

To solve the question, we need to understand the relationship between pressure, volume, and temperature of a gas. The question states that at constant temperature, the product of pressure and volume of a given amount of gas is constant. We will analyze this step by step.

### Step 1: Identify the Conditions
The question specifies that the temperature is constant. This is a crucial detail because it indicates that we are dealing with a specific gas law that applies under isothermal conditions (constant temperature).

**Hint:** Look for gas laws that specifically mention constant temperature.

### Step 2: Recall Relevant Gas Laws
There are several gas laws, but the most relevant ones in this context are:
- Boyle's Law: States that at constant temperature, the pressure of a gas is inversely proportional to its volume. Mathematically, this can be expressed as \( P \times V = k \) (where \( k \) is a constant).
- Charles's Law: Relates volume and temperature at constant pressure.
- Gay-Lussac's Law: Relates pressure and temperature at constant volume.

**Hint:** Focus on the law that relates pressure and volume while keeping temperature constant.

### Step 3: Apply Boyle's Law
According to Boyle's Law, if the temperature is held constant, then the product of pressure (P) and volume (V) for a fixed amount of gas remains constant. Therefore, if the volume increases, the pressure decreases, and vice versa.

**Hint:** Remember that Boyle's Law is about the inverse relationship between pressure and volume at constant temperature.

### Step 4: Eliminate Incorrect Options
- **Charles's Law** cannot be the answer because it deals with volume and temperature at constant pressure.
- **Gay-Lussac's Law** cannot be the answer because it deals with pressure and temperature at constant volume.
- The option "none of these" is also incorrect as we have identified Boyle's Law as the correct answer.

**Hint:** Use the definitions of each law to eliminate options that do not fit the conditions given in the question.

### Conclusion
The correct answer to the question is **Boyle's Law**, which states that at constant temperature, the product of pressure and volume of a given amount of gas is constant.

**Final Answer:** Boyle's Law