If a gas expands at constant temperature

Options

A. the pressure decreases
B. the kinetic energy of the molecules remains the same
C. the K.E. of the molecules decrease
D. the number of molecules of the gas increase

Explanation

To solve the problem of a gas expanding at constant temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Ideal Gas Law**:
The ideal gas law is given by the equation:
\[ PV = nRT \]
where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles of gas, \( R \) is the universal gas constant, and \( T \) is the absolute temperature.

2. **Identifying Constant Parameters**:
In this scenario, the temperature \( T \) is constant, which implies that \( nRT \) is also constant since \( n \) (number of moles) and \( R \) (gas constant) do not change.

3. **Analyzing the Relationship Between Pressure and Volume**:
Since \( nRT \) is constant, we can express the relationship between pressure and volume as:
\[ PV = \text{constant} \]
This means that if the volume \( V \) increases, the pressure \( P \) must decrease to keep the product \( PV \) constant.

4. **Understanding Kinetic Energy**:
The kinetic energy of gas molecules is given by:
\[ KE = \frac{3}{2} nRT \]
Since the temperature \( T \) is constant, the kinetic energy of the gas molecules remains constant throughout the expansion.

5. **Conclusion**:
Therefore, when a gas expands at constant temperature, its pressure decreases while the kinetic energy of the gas molecules remains unchanged.

### Final Statements:
- As the volume increases, the pressure decreases (Boyle's Law).
- The kinetic energy of the gas molecules remains constant since the temperature is constant.

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