If a gas is allowed to expand at constant temperature, then :

Options

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

Answer

To solve the question, let's analyze the situation step by step.

### Step 1: Understand the conditions of the problem
The question states that a gas is allowed to expand at constant temperature. This means that the temperature of the gas does not change during the process.

**Hint:** Remember that constant temperature implies an isothermal process.

### Step 2: Recall the relationship between temperature and kinetic energy
The kinetic energy (KE) of gas molecules is directly related to the temperature of the gas. The formula for the average kinetic energy of a gas is given by:
\[ KE = \frac{3}{2} RT \]
where \( R \) is the gas constant and \( T \) is the absolute temperature in Kelvin.

**Hint:** Kinetic energy is proportional to temperature; if temperature is constant, kinetic energy remains constant.

### Step 3: Analyze the implications of constant temperature
Since the temperature is constant during the expansion, the average kinetic energy of the gas molecules must also remain constant. This means that even though the gas is expanding, the energy associated with the motion of the molecules does not change.

**Hint:** Think about what happens to the speed of molecules when temperature is constant.

### Step 4: Conclusion
Based on the above analysis, we can conclude that the kinetic energy of the gas molecules remains the same when the gas expands at constant temperature. Therefore, the correct answer to the question is that the kinetic energy of a gas molecule remains the same.

**Final Answer:** The kinetic energy of a gas molecule remains the same.