According to the Maxwellian speed distribution, as the temperature increases the most probable speed

Options

A. increases
B. decreases
C. increases at high temperatures and decreases at low
D. decreases at high temperatures and increases at low.

Answer

To solve the question regarding the relationship between temperature and the most probable speed according to the Maxwellian speed distribution, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Most Probable Speed**:
- The most probable speed is defined as the speed at which the maximum number of molecules in a gas sample are moving. It can be derived from the Maxwell-Boltzmann distribution of speeds.

2. **Expression for Most Probable Speed**:
- The formula for the most probable speed (\(v_{mp}\)) of gas molecules is given by:
\[ v_{mp} = \sqrt{\frac{2RT}{M}} \]
where:
- \(R\) is the universal gas constant,
- \(T\) is the absolute temperature in Kelvin,
- \(M\) is the molar mass of the gas.

3. **Analyzing the Effect of Temperature**:
- From the formula, we can see that the most probable speed is directly proportional to the square root of the temperature (\(T\)). This means that as the temperature increases, the most probable speed also increases.

4. **Conclusion**:
- Therefore, we can conclude that as the temperature increases, the most probable speed of the gas molecules also increases.

### Final Answer:
According to the Maxwellian speed distribution, as the temperature increases, the most probable speed increases.

---