The effect of temperature on Maxwell's speed distribution is correctly shown by

Options

A.
B.
C.
D.

Answer

To determine the effect of temperature on Maxwell's speed distribution, we need to analyze the Maxwell-Boltzmann distribution function and how it changes with temperature.

### Step-by-Step Solution:

1. **Understand Maxwell's Speed Distribution**:
The Maxwell-Boltzmann distribution describes the distribution of speeds (or velocities) of particles in a gas. The mathematical expression is given by:
\[ f(v) = \frac{n}{(2 \pi k T)^{3/2}} \cdot 4 \pi v^2 \cdot e^{-\frac{mv^2}{2kT}} \]
where \( f(v) \) is the probability density function, \( n \) is the number of particles, \( m \) is the mass of the particles, \( k \) is the Boltzmann constant, \( T \) is the absolute temperature, and \( v \) is the speed.

2. **Analyze the Effect of Temperature**:
From the equation, we can see that temperature \( T \) appears in the denominator of the exponent. This indicates that as temperature increases, the exponent becomes less negative, leading to a higher probability of finding particles at higher speeds.

3. **Graph Characteristics**:
- At higher temperatures, the distribution curve shifts to the right, indicating that particles have higher average speeds.
- The peak of the distribution (the most probable speed) decreases with increasing temperature, meaning that while more particles are moving at higher speeds, the most probable speed is not the same.

4. **Comparing Graphs**:
We need to compare the graphs provided in the options. We are looking for:
- A graph where the curve for higher temperature (T1) is shifted to the right compared to the lower temperature (T2).
- The peak of the distribution for T1 should be lower than that for T2, indicating that while more particles are moving faster, the most probable speed is lower.

5. **Identifying the Correct Graph**:
- In the first graph, T1 (higher temperature) has a peak that is lower than T2, and the distribution is shifted to the right, which is consistent with our understanding.
- In the second graph, T1 has a higher peak than T2, which contradicts the expected behavior.
- The third and fourth graphs can be eliminated based on similar reasoning.

6. **Conclusion**:
The correct graph that shows the effect of temperature on Maxwell's speed distribution is the first graph, where T1 is greater than T2, and the peak for T1 is lower than that for T2.

### Final Answer:
The effect of temperature on Maxwell's speed distribution is correctly shown by **option number one**.