If a gas is allow to expand at constant temperature,

Options

A. the pressure decreases
B. the kinetic energy of the molecules remains the same
C. kinetic energy decreases
D. no. of molecules of the gas increases.

Explanation

To solve the question, "If a gas is allowed to expand at constant temperature, what will happen?", we can analyze the situation using Boyle's Law and the relationship between pressure, volume, and temperature.

### Step-by-Step Solution:

1. **Understanding Boyle's Law**:
- Boyle's Law states that for a given mass of gas at constant temperature, the pressure (P) of the gas is inversely proportional to its volume (V). This can be mathematically expressed as:
\[ P \propto \frac{1}{V} \quad \text{or} \quad PV = k \]
where \( k \) is a constant.

**Hint**: Remember that Boyle's Law applies only when the temperature is constant.

2. **Analyzing the Expansion**:
- If the gas is allowed to expand, it means that the volume (V) is increasing. According to Boyle's Law, if the volume increases, the pressure (P) must decrease to maintain the relationship \( PV = k \).

**Hint**: Think about how increasing one variable affects the other in an inverse relationship.

3. **Kinetic Energy Consideration**:
- The kinetic energy of gas molecules is given by the formula:
\[ KE = \frac{3}{2} RT \]
where \( R \) is the gas constant and \( T \) is the absolute temperature. Since the temperature is constant during the expansion, the kinetic energy of the gas molecules will also remain constant.

**Hint**: Kinetic energy is directly related to temperature; if temperature is constant, kinetic energy does not change.

4. **Number of Molecules**:
- The number of molecules in the gas does not change during the expansion process. The gas is simply occupying a larger volume, but the amount of gas (number of molecules) remains the same.

**Hint**: Consider what happens to the quantity of gas when it expands in volume.

5. **Conclusion**:
- From the analysis, we can conclude:
- The pressure decreases as the volume increases (True).
- The kinetic energy of the molecules remains the same (True).
- The kinetic energy does not decrease (False).
- The number of molecules does not increase (False).

### Final Answer:
- The correct statements are:
- A: Pressure decreases as volume increases (True).
- B: Kinetic energy remains the same (True).

Thus, the correct options are A and B.