The temperature of a gas is raised while its volume remains constant, the pressure exerted by the gas on the walls of the container increases because its molecules

Options

A. lose more kinetic energy to the wall
B. are in contact with the wall for a shorter time
C. strike the wall more often with higher velocities
D. collide with each other with less frequency

Explanation

To solve the question regarding the increase in pressure exerted by a gas when its temperature is raised at constant volume, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship Between Pressure, Volume, and Temperature:**
The ideal gas law states that \( PV = nRT \), where:
- \( P \) = Pressure of the gas
- \( V \) = Volume of the gas
- \( n \) = Number of moles of the gas
- \( R \) = Universal gas constant
- \( T \) = Absolute temperature of the gas

Since the volume \( V \) is constant, any increase in temperature \( T \) will result in an increase in pressure \( P \).

2. **Effect of Temperature on Molecular Speed:**
The root mean square speed (\( v_{rms} \)) of gas molecules is given by the formula:
\[ v_{rms} = \sqrt{\frac{3RT}{m}} \]
where \( m \) is the mass of a gas molecule. As the temperature \( T \) increases, \( v_{rms} \) also increases.

3. **Increased Molecular Speed Leads to More Collisions:**
With an increase in molecular speed, the gas molecules collide with the walls of the container more frequently and with greater force. This is because faster-moving molecules hit the walls more often and with greater momentum.

4. **Pressure Increase Due to More Frequent Collisions:**
The pressure exerted by the gas on the walls is a result of these collisions. Therefore, as the temperature increases, the increase in molecular speed leads to more frequent and forceful collisions with the walls, which in turn increases the pressure.

5. **Conclusion:**
Thus, the pressure exerted by the gas on the walls of the container increases because the molecules strike the walls more often and with higher momentum due to their increased speed from the rise in temperature.

### Final Answer:
The pressure exerted by the gas on the walls of the container increases because its molecules strike the wall more often with higher momentum.

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