Home
Class 12
PHYSICS
Which of the following plot is correct a...

Which of the following plot is correct about Maxwell's speed distribution low ?

A

B

C

D

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question regarding Maxwell's speed distribution law, we need to analyze the relationship between the most probable speed, average speed, and root mean square (RMS) speed of gas molecules. Here’s a step-by-step breakdown of the solution: ### Step 1: Understand the Definitions 1. **Most Probable Speed (v_mp)**: This is the speed at which the maximum number of molecules are found. It corresponds to the peak of the distribution curve. 2. **Average Speed (v_avg)**: This is the mean speed of all the molecules in the gas. 3. **Root Mean Square Speed (v_rms)**: This is the square root of the average of the squares of the speeds of the molecules. ### Step 2: Recall the Formulas The formulas for these speeds in terms of temperature (T) and molecular mass (M) are: - \( v_{rms} = \sqrt{\frac{3RT}{M}} \) - \( v_{avg} = \sqrt{\frac{8RT}{\pi M}} \) - \( v_{mp} = \sqrt{\frac{2RT}{M}} \) ### Step 3: Compare the Speeds To compare these speeds, we can derive the ratios: - \( v_{rms} : v_{avg} : v_{mp} = \sqrt{3} : \sqrt{\frac{8}{\pi}} : \sqrt{2} \) Calculating the approximate values: - \( \sqrt{3} \approx 1.732 \) - \( \sqrt{\frac{8}{\pi}} \approx 1.595 \) - \( \sqrt{2} \approx 1.414 \) From this, we can see that: - \( v_{rms} > v_{avg} > v_{mp} \) ### Step 4: Analyze the Graphs In the context of the graphs provided: - The x-axis represents speed, and the y-axis represents the fractional number of molecules. - The peak of the graph should correspond to the most probable speed, which is the highest point on the curve. - The average speed should be to the right of the most probable speed, and the RMS speed should be to the right of the average speed. ### Step 5: Identify the Correct Plot Based on the analysis: - The correct plot will have the peak at the most probable speed, followed by the average speed, and then the RMS speed. ### Conclusion Thus, the correct option among the provided graphs is the one where: - Most Probable Speed (peak) < Average Speed < RMS Speed.
Promotional Banner

Similar Questions

Explore conceptually related problems

Which of the following is correct about biogas-

Which of the following plots is/are correct?

Which of the following plots is/are correct?

Which of the following is correct about growth?

Which of the following is correct about symplast?

Which of the following is not correct about DNA?

Which of the following is correct about legumes?

which of the following is correct about viroids?

Which of the followings is not correct about colloids?

Which of the following is correct about dinoflagellates?