If a gas expands at constant temperature, it indicates that

Options

A. kinetic energy of molecules remains the same
B. number of the molecules of gas increases
C. kinetic energy of molecules decreases
D. pressure of the gas increases

Explanation

To solve the question regarding the behavior of a gas that expands at constant temperature, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding Constant Temperature Expansion**:
- When a gas expands at constant temperature, it is undergoing an isothermal process. In this process, the temperature (T) of the gas does not change.

2. **Applying Boyle's Law**:
- According to Boyle's Law, for a given amount of gas at constant temperature, the product of pressure (P) and volume (V) is constant. This can be expressed as:
\[ PV = \text{constant} \]
- Therefore, if the volume (V) increases during the expansion, the pressure (P) must decrease to maintain the equality.

3. **Analyzing Pressure and Volume Relationship**:
- Since the gas is expanding, we can conclude that:
- As \( V \) increases, \( P \) must decrease.
- This indicates an inverse relationship between pressure and volume when temperature is held constant.

4. **Kinetic Energy Consideration**:
- The average kinetic energy of gas molecules is directly proportional to the temperature of the gas. Since the temperature remains constant during the isothermal expansion, the average kinetic energy of the molecules also remains constant.
- The formula for the average kinetic energy (KE) of gas molecules is given by:
\[ KE = \frac{3}{2} k_B T \]
where \( k_B \) is the Boltzmann constant and \( T \) is the absolute temperature.

5. **Conclusion**:
- Therefore, during the isothermal expansion of a gas:
- The pressure decreases as the volume increases.
- The average kinetic energy of the gas molecules remains constant.

### Final Answer:
If a gas expands at constant temperature, it indicates that the pressure of the gas decreases while the average kinetic energy of the molecules remains constant.