At any particular time , different particles in the gas

Options

A. have same speed and kinetic energy
B. have same speed but different kinetic energies
C. have different speeds nut same kinetic energy
D. have different speeds and hence different kinetic energies .

Explanation

To solve the question regarding the behavior of gas particles at any particular time, we can analyze the options provided based on the principles of the kinetic theory of gases.

### Step-by-Step Solution:

1. **Understanding Gas Behavior**: According to the kinetic theory of gases, gas particles are in constant random motion. They move in all directions and collide with each other and the walls of the container.

2. **Analyzing the Options**:
- **Option A**: "Have same speed and kinetic energy."
- This option suggests that all gas particles have the same speed and kinetic energy. This is incorrect because, due to random motion and collisions, gas particles will have different speeds.

- **Option B**: "Have same speed but different kinetic energies."
- If particles have the same speed, they must also have the same kinetic energy (since kinetic energy is dependent on speed). Therefore, this option is also incorrect.

- **Option C**: "Have different speeds and same kinetic energies."
- Different speeds would lead to different kinetic energies. Hence, this option is incorrect as well.

- **Option D**: "Have different speeds and hence different kinetic energies."
- This option aligns with the kinetic theory of gases. Since gas particles are in random motion and collide with each other, they will have different speeds, which leads to different kinetic energies.

3. **Conclusion**: Based on the analysis, the correct answer is **Option D**: "Have different speeds and hence different kinetic energies."